Johannes H. Hattingh

Curriculum Vitae

May 2008

  1. Education
  2. Professional Experience
  3. Professional Service
  4. Current Research Interests
  5. Honors and Awards
  6. Research Grants
  7. Professional Society Memberships
  8. Students
  9. Papers Presented
  10. Publications

EDUCATION

B.Sc. (Mathematical Sciences) (1984) (cum laude), University of Johannesburg  (formerly known as Rand Afrikaans University)
B.Sc. Honours (Mathematics) (1985) (cum laude), University of Johannesburg
M.Sc. (Mathematics) (1986) (cum laude) University of Johannesburg
Ph.D. (Mathematics) (1989) University of Johannesburg
B.Sc. Honours (cum laude) (Computer Science) (1994) University of Johannesburg

PROFESSIONAL EXPERIENCE

Lecturer, University of Pretoria, July 1988 - June 1989
Lecturer, University of Johannesburg, July 1989 - December 1989
Senior Lecturer, University of Johannesburg, January 1990 - March 1993
Associate Professor, University of Johannesburg, April 1993 - March 1998
Assistant Professor, Georgia State University, July 1997 - June 2001
Associate Professor, Georgia State University , July 2001 - June 2006
Acting Chair, Georgia State University, January 2004- September 2004
Chair, Georgia State University, October 2004 – present
Professor, Georgia State University , July 2006 – present

PROFESSIONAL SERVICE

Referee for Acta Mathematica Sinica, AKCE International Journal of Graphs and Combinatorics, Applied Mathematics Letters, Ars Combinatoria, The Australasian Journal of Combinatorics, The Computer Journal, Discrete Applied Mathematics, Discrete Mathematics, Discrete Mathematics and Theoretical Computer Science,  Discussiones Mathematicae, The Electronic Journal of Combinatorics, Graphs and Combinatorics, Journal of Combinatorial Mathematics and Combinatorial Computing, Journal of Combinatorial Optimization, Journal of Graph Theory, Journal of Integer Sequences, Mathematica Slovaca, Quaestiones Mathematicae, SIAM Journal on Discrete Mathematics, The South African Computer Journal and Utilitas Mathematica.

I was a co-organizer of the 16th Cumberland Conference on Combinatorics, Graph Theory, and Computing held on the campus of Georgia State University from May 15 to May 17, 2003.

CURRENT RESEARCH INTEREST

Research in Graph Theory with an emphasis on domination in graphs.

HONORS, AWARDS

President's Award, Foundation of Research Development, August 1994 - March 1998

RESEARCH GRANTS

Y-researcher, Foundation of Research Development. August 1990 - July 1994
President's Award, Foundation of Research Development, August 1994 - March 1998

PROFESSIONAL SOCIETIES MEMBERSHIP

I am a member of the American Mathematical Society and a Fellow of the Institute of Combinatorics and its applications.

STUDENTS

MASTERS

  1. Mr. A. Barnard, M.Sc. (Mathematics) (Rand Afrikaans University, 1990) Die grafiek-isomorfie probleem. (Served as co-supervisor with Prof. A. Buys as supervisor.)
  2. Mr. A. Barnard, M.Sc. (Computer Science) (Rand Afrikaans University, 1991) 'n Verdere uitbreiding van struktuurgrafiekgrammatikas. (Served as co-supervisor with Prof. E. Ehlers as supervisor.)
  3. Miss. E. Jonck, M.Sc. (Rand Afrikaans University, 1992) Kompleksiteitsaspekte van veralgemeende dominasieparameters.
  4. Mr. J. C. Schoeman, M.Sc. (Rand Afrikaans University, 1993) 'n Ry boonste en onderste dominasie- onafhanklikheids- en onoorbodigheidsgetalle van 'n grafiek.
  5. Mr. R. van der Merwe, M.Sc (Computer Science) (Rand Afrikaans University, 1993) The use of fractals, wavelet coding and learning automata in image compression. (Served as co-supervisor with Prof. E. Ehlers as supervisor.)
  6. Mr. F. A. Lategan, M.Sc. (Rand Afrikaans University, 1995) Complexity aspects of certain graphical parameters.
  7. Mr. V. Vuong, M.S. (Georgia State University, 1999) Domination in graph with bounded degrees.
  8. Mr. Andrew R. Plummer M.S. (Georgia State University, 2006) Characterizations in domination theory.

DOCTORAL

  1. Mrs. E. Ungerer, Ph.D. (Rand Afrikaans University, 1996) Aspects of signed and minus domination in graphs.
  2. Mrs. L.M. Harris, Ph.D. (University of Natal, Pietermaritzburg, 2003) Aspects of functional variations of domination in graphs. (Served as co-supervisor with Prof. M.A. Henning.)
  3. Mr E.J. Joubert, Ph.D. (University of Johannesburg, 2008) Aspects of total restrained domination in graphs. (Served as co-supervisor with Prof. E. Jonck.)
  4. Mr.C. J. Ras, Ph.D. (University of Johannesburg, 2008) $\lambda_{d,1}$-minimal trees and full colorability of some classes of graphs. (Served as co-supervisor with Prof. E. Jonck.)

PAPERS PRESENTED

  1. Annual meeting of the SAMS, Pretoria, S Africa, 1985 (with J. Heidema) Relatiewe semantiese afleibaarheid.
  2. Graph Theory Workshop, Pretoria, S Africa,  1988 (with I. Broere) Products of circulant graphs.
  3. Annual meeting of the SAMS, Stellenbosch, S Africa, 1988 The edge-chromatic number of a circulant.
  4. Annual meeting of the SAMS, Stellenbosch, S Africa, 1988 (with I. Broere) Hamilton properties and the chromatic index of an abelian Cayley graph.
  5. Annual meeting of the SAMS, Bloemfontein, S Africa, 1990 On irredundant Ramsey numbers for graphs.
  6. 21st SE International Congress on Combinatorics, Graph Theory and Computing, Boca Raton, FL, USA, 1990 (with E.J. Cockayne and C.M. Mynhardt) The irredundant Ramsey number s(3,7).
  7. 255th Anniversary of Graph Theory, Durban, S Africa, 1991 (with G. Chen and C.C. Rousseau) Asymtotic bounds for irredundant and mixed Ramsey numbers.
  8. Annual meeting of the SAMS, Mmbatho, S Africa, 1991 Lower bounds for diagonal irredundant Ramsey numbers.
  9. 23rd SE International Congress on Combinatorics, Graph Theory and Computing, Boca Raton, FL, USA, 1992 (with M.A. Henning) Distance irredundance in graphs: complexity issues.
  10. 18th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, Perth, Australia, 1992 (with M.A. Henning) Distance irredundance number versus distance domination number.
  11. Annual meeting of the SAMS, Cape Town, S Africa, 1992 (with M.A. Henning) Distance irredundance number versus distance domination number.
  12. 24th SE International Congress on Combinatorics, Graph Theory and Computing, Boca Raton, FL, USA, 1993 (with M.A. Henning and J.C. Schoeman) On a sequence of generalised domination numbers.
  13. Annual meeting of the SAMS, Pretoria, S Africa, 1993 (with M.A. Henning and J.L. Walters) On the computational complexity of upper distance fractional domination.
  14. Annual meeting of the SAMS, Pretoria, S Africa, 1993 (with P. Erdös) Asymtotic bounds for irredundant Ramsey numbers.
  15. 9th Mini-conference on Discrete Mathematics, Clemson, SC, USA, October 1994 Majority domination and its generalisations (this was an invited talk).
  16. 26th SE International Congress on Combinatorics, Graph Theory and Computing, Boca Raton, FL, USA, 1995 (with R.C. Laskar) On weak domination in graphs.
  17. 15th British Combinatorial Conference, Stirling, UK, 1995 (with J.E. Dunbar, J. W. Grossman, S.T. Hedetniemi and A.A. McRae) On weakly-connected domination in graphs.
  18. Eighth International Conference on Graph Theory. Combinatorics, Algorithms and Applications, Kalamazoo, MI, USA, June 1996 (with E. Ungerer) On signed k-subdomination in graphs.
  19. Annual meeting of the SAMS, Bellville, S Africa, 1996 (with J.E. Dunbar, A. A. McRae and P.J. Slater) Efficient coverage of edge sets in graphs.
  20. 28th SE International Congress on Combinatorics, Graph Theory and Computing, Boca Raton, FL, USA, 1997 (with J. E. Dunbar, A. A. McRae and P. J. Slater) Efficient coverage of edge sets in graphs.
  21. 29th SE International Congress on Combinatorics, Graph Theory and Computing, Boca Raton, FL, USA, 1998 (with G. S. Domke, M. A. Henning and L. R. Markus) Restrained domination in trees.
  22. 29th SE International Congress on Combinatorics, Graph Theory and Computing, Boca Raton, FL, USA, 1998 (with G. S. Domke, S.T. Hedetniemi, R.C. Laskar and L. R. Markus) Restrained domination in graphs.
  23. 11th Cumberland Conference on Graph Theory, Combinatorics, and Computing, Johnson City, TN, USA, 1998 (with D. Rautenbach) On weak domination in graphs II.
  24. 11th Cumberland Conference on Graph Theory, Combinatorics, and Computing, Johnson City, TN, USA, 1998 (with G.S. Domke, L.R. Markus and E. Ungerer) Gallai-type theorems for strong and weak domination parameters.
  25. Annual meeting of the SAMS, Pietersburg, S Africa, 1999 (with G. Chen, G.S. Domke and R.C. Laskar) On line-distinguishing and harmonious colorings of a graph.
  26. 5th Annual Mini-Conference on Graph Theory, Boone, NC, USA, 2000 (with E. Ungerer) On line-distinguishing and harmonious colorings of a graph II.
  27. 9th Quadrennial International Conference on Graph Theory, Combinatorics, Algorithms and Applications, Kalamazoo, MI, USA, 2000 (with I. Broere, M. Dorfling and E. Ungerer) Partitioning a tree into two restrained dominating sets.
  28. 15th Clemson mini-Conference on Discrete Mathematics, Clemson, SC, USA, 2000 A Survey of Minus and Signed Domination in Graphs (this was an invited talk).
  29. South African International Graph Theory Conference, Ithala Game Reserve, S Africa, 2001 An overview of restrained domination in graphs (this was an invited talk).
  30.  Regional meeting of the AMS, Chattanooga, TN, USA, 2001(with M.A. Henning and E. Ungerer) Graphs with small upper line-distinguishing and upper harmonious chromatic numbers (this was an invited talk).
  31.  Regional meeting of the AMS, Atlanta, GA,  USA, 2002 (with I. Broere, M. Dorfling, W. Goddard, M.A. Henning and E. Ungerer) Graphs with two disjoint total dominating sets (this was an invited talk)
  32.  DCI '02 Research Program, DIMACS, Rutgers University, Piscataway, NJ,  USA,   2002  (with L. Harris) The algorithmic complexity of certain functional variations of total domination in graphs (I was invited to attend).
  33. Joint MAA-SAIM Meeting at Clemson University, Clemson, SC, USA,  2003 (with L. Harris and M.A. Henning)  Total k-subdominating functions on graphs (this was an invited talk).
  34. 19th British Combinatorial Conference,  Bangor, UK, 2003 (with L. Harris and M.A. Henning) Algorithmic aspects of total k-subdomination in graphs.
  35. 35th SE International Congress on Combinatorics, Graph Theory and Computing, Boca Raton, FL, USA, 2004 (with G. S. Domke and L. R. Markus) On weakly connected domination in graphs II.
  36. 28th annual SIAM Southeastern Atlantic Section Meeting, Johnson City, TN, USA, 2004 (with G. S. Domke and L. R. Markus) On weakly connected domination in graphs II  (I was invited to attend).
  37. 36th SE International Congress on Combinatorics, Graph Theory and Computing, Boca Raton, FL, USA, 2005 (with P. Dankelmann, M. A. Henning and H. C. Swart) Trees with equal domination and restrained domination numbers.
  38. 18th Cumberland Conference on Graph Theory, Combinatorics, and Computing, Huntsville, AL, USA, 2005 (with E. Jonck and C. Ras) The L(d,1)-hole index of paths and cycles.
  39. 37th SE International Congress on Combinatorics, Graph Theory and Computing, Boca Raton, FL, USA, 2006 (with E. Jonck, E.J. Joubert and A.R. Plummer) Total restrained domination in trees.
  40. 19th Cumberland Conference on Graph Theory, Combinatorics, and Computing, Johnson City, TN, USA, 2006 (with E. Jonck, E.J. Joubert and A.R. Plummer) Nordhaus-Gaddum results for restrained domination and total restrained domination in graphs.
  41. International Conference on Discrete Mathematics (ICDM 2006), Bangalore, India, December 2006, Restrained domination in graphs (this was an invited talk).

PUBLICATIONS

  1. The edge-chromatic number of a circulant, Quaestiones Mathematica 11 (1988) 371 - 381.
  2. (with I. Broere) Products of circulant graphs, Quaestiones Mathematica 13 (1990) 191 - 216.
  3. (with E.J. Cockayne, J. Kok and C.M. Mynhardt) Mixed Ramsey numbers and irredundant Turán numbers for graphs, Ars Combinatoria 29 (1990) 57 - 68.
  4. On irredundant Ramsey numbers for graphs, Journal of Graph Theory 14 (1990) 437 - 441.
  5. (with I. Broere) The chromatic index of an abelian Cayley graph, Ars Combinatoria 31 (1991) 312 - 316.
  6. (with E.J. Cockayne and C.M. Mynhardt) The irredundant Ramsey number s(3,7), Utilitas Mathematica 39 (1991) 145 - 160.
  7. (E.J. Cockayne, G. Exoo and C.M. Mynhardt) The irredundant Ramsey number s(4,4), Utilitas Mathematica 41 (1992) 119 - 128.
  8. (with M.A. Henning) The complexity of upper distance irredundance, Congressus Numerantium 91 (1992) 107 - 115.
  9. (with A. Barnard and E.M. Ehlers) A further extention of structure graph grammars, Information Sciences 73 (1993) 235-271.
  10. (with G. Chen and C.C. Rousseau) Asymtotic bounds for irredundant and mixed Ramsey numbers, Journal of Graph Theory 17 (1993) 193 - 206.
  11. (with P. Erdös) Asymtotic bounds for irredundant Ramsey numbers, Quaestiones Mathematica 16 (1993) 319-331.
  12. (with M.A. Henning) A characterization of block graphs that are well-k-dominated, Journal of Combinatorial Mathematics and Combinatorial Computing 13 (1993) 33 - 38.
  13. (with M.A. Henning and J.L. Walters) On the complexity of distance upper fractional domination, Australasian Journal of Combinatorics 7 (1993) 133-144.
  14. (with M.A. Henning) The ratio of distance irredundance and domination numbers, Journal of Graph Theory 18 (1994) 1 - 9.
  15. (with M.A. Henning and P.J. Slater) Minus k-neighbourhood domination in graphs, The Australasian Journal of Combinatorics 9 (1994) 233-242.
  16. (with I. Broere) On the construction of self- complementary circulant graphs, Graph Theory, Combinatorics and Applications John Wiley and Sons 1 (1995) 123-129.
  17. (with I. Broere, M.A. Henning and A.A. McRae) Majority domination in graphs, Discrete Mathematics 138 (1995) 125-135.
  18. (with M.A. Henning) Distance irredundance in graphs Graph Theory, Combinatorics and Applications John Wiley and Sons 1 (1995) 529-541.
  19. (with M.A. Henning and P.J. Slater) The algorithmic complexity of signed domination in graphs, The Australasian Journal of Combinatorics 12 (1995) 101-112.
  20. (with E. J. Cockayne, S.M. Hedetniemi, S.T. Hedetniemi and A.A. McRae) Using maximality and minimality conditions to construct inequality chains, Discrete Mathematics 176 (1997) 43-61.
  21. (with J.E. Dunbar, J.W. Grossman, S.T. Hedetniemi and A.A. McRae) On weakly-connected domination in graphs, Discrete Mathematics 167-168 (1997) 261-269.
  22. (with J.E. Dunbar, P.J. Slater and A.A. McRae) Efficient coverage of edge sets in graphs, Utilitas Mathematica 51 (1997) 183-192.
  23. Majority domination and its generalisations, Domination in graphs: Advanced topics Marcel-Dekker Inc. (1997), 91-108.
  24. (with E. Ungerer) Minus k-subdomination in graphs II, Discrete Mathematics 171 (1997) 141-151.
  25. (with I. Broere and J.E. Dunbar) Minus k-subdomination in graphs, Ars Combinatoria 50 (1998) 177-186.
  26. (with M. A. Henning) Star-bipartite Ramsey numbers, Discrete Mathematics 185 (1998) 255-258.
  27. (with M.A. Henning) Bipartite Ramsey Theory, Utilitas Mathematica 53 (1998) 217-230.
  28. (with M. A. Henning) On strong domination in graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 26 (1998), 73-82.
  29. (with M.A. Henning and E. Ungerer) Partial signed domination in graphs, Ars Combinatoria 48 (1998) 33-42.
  30. (with M.A. Henning and J.L Walters) Distance irredundance in graphs: complexity issues, Ars Combinatoria 50 (1998) 3-22.
  31. (with R.C. Laskar) On weak domination in graphs, Ars Combinatoria 49 (1998) 205-216.
  32. (with A.A. McRae and E. Ungerer) Minus k-subdomination in graphs III, Australasian Journal of Combinatorics 17 (1998), 69-76.
  33. (with A.A. McRae and E. Ungerer) The minus bondage number of a graphs, Proceedings of the Eighth Quadrennial International Conference on Graph Theory, Combinatorics, Algorithms and Applications II (1998) 491-503.
  34. (with E. Ungerer) The signed and minus k-subdomination numbers of comets, Discrete Mathematics 183 (1998) 141-152.
  35. (with E. Ungerer) On the signed k-subdomination number of trees, Proceedings of the Eighth Quadrennial International Conference on Graph Theory, Combinatorics, Algorithms and Applications II (1998)479-490.
  36. (with G. Chen, G.S. Domke and R.C. Laskar) On the upper line-distinguishing and upper harmonious chromatic numbers of a graph, Journal of Combinatorial Mathematics and Combinatorial Mathematics 31 (1999) 227-239.
  37. (with G.S. Domke, S.T. Hedetniemi, R.C. Laskar and L.R. Markus) Restrained domination in graphs, Discrete Mathematics 203 (1999) 61-69.
  38. (with J.E. Dunbar, R.C. Laskar and L.R. Markus) Induced clique domination in graphs, Ars Combinatoria 52 (1999) 129-139.
  39. (with G.S. Domke, M.A. Henning and L.R. Markus) Restrained domination in trees, Discrete Mathematics 211(2000) 1-9.
  40. (with G.S. Domke, M.A. Henning and L.R. Markus) Restrained domination in graphs with minimum degree two, Journal of Combinatorial Mathematics and Combinatorial Computing 35(2000) 239-254.
  41. (with G.S. Domke and L.R. Markus) On the number of edges in a graph with given domination-type parameters, Journal of Combinatorial Mathematics and Combinatorial Computing 33 (2000) 23-32.
  42. (with M.A. Henning) Characterizations of trees with equal domination parameters, Journal of Graph Theory 34 (2000) 142-153.
  43. (with L.M. Harris and E. Ungerer) The signed and minus k-subdomination number of certain multipartite graphs and their complement, Utilitas Mathematica 59 (2001) 77-95.
  44. (with G.S. Domke, L.R. Markus and E. Ungerer) On parameters related to strong and weak domination in graphs, Discrete Mathematics 258 (2002) 1-11.
  45. (with D. Rautenbach) Further results on weak domination in graphs, Utilitas Mathematica 61 (2002) 193-207.
  46. (with M.A. Henning and E. Ungerer) The upper line-distinguishing and upper harmonious chromatic numbers of a cycle,  Journal of Combinatorial Mathematics and Combinatorial Computing 45 (2003) 139-146.
  47. (with M.A. Henning and E. Ungerer) Graphs with small upper line-distinguishing and upper harmonious chromatic numbers, Journal of Combinatorial Mathematics and Combinatorial Computing 47 (2003) 165-181.
  48. (with I. Broere, M. Dorfling, W. Goddard, M.A. Henning and E. Ungerer) Augmenting trees to have two disjoint total dominating sets, The Bulletin of the Institute of Combinatorics and its Applications 42 (2004) 12-18.
  49. (with P. Dankelmann, G.S. Domke, W. Goddard, P. Grobler and H.C. Swart) Maximum sizes for domination parameters, Discrete Mathematics, 281 (2004) 137-148.
  50. (with L.M. Harris) The algorithmic complexity of certain functional variations of total domination in graphs, Australasian Journal of Combinatorics 29 (2004) 143-156.
  51. (with G.S. Domke and L.R. Markus) On weakly connected domination in graphs II, Discrete Mathematics  305 (2005) 112-122.
  52. (with W. Goddard and M.A. Henning) Augmenting a graph of minimum degree 2 to have two disjoint total dominating sets, Discrete Mathematics 300 (2005) 82-90
  53. (with P. Dankelmann, M. A. Henning and H. C. Swart) Trees with equal domination and restrained domination numbers, Journal of Global Optimization 34 (2006), 597-607.
  54. (with L.M. Harris and M.A. Henning) Total k-subdominating functions on graphs, Australasian Journal of Combinatorics, 35 (2006) 141-154.
  55. (with L.M. Harris and M.A. Henning) Algorithmic aspects of total k-subdomination in graphs, Discussiones Mathematicae Graph Theory 26(1) (2006) 5-18.
  56. (with L.M. Harris and M.A. Henning) Algorithmic aspects of minus total k-subdomination in graphs, Australasian Journal of Combinatorics 36 (2006) 101-111.
  57. (with E. Jonck and C. Ras) The L(d,1)-hole index of paths and cycles, Utilitas Mathematica 69 (2006) 55-64.
  58. (with E. Jonck, E. Joubert and A.R. Plummer) Total restrained domination in trees, Discrete Mathematics  307 (2007) 1643-1650.
  59. (with P. Dankelmann, D. Day, M. A. Henning, L R. Markus and H. C. Swart) On equality in an upper bound for the restrained and total domination numbers of a graph, Discrete Mathematics 307 (2007) 2845-2852.
  60.  (with E. Jonck, E. J. Joubert and A.R. Plummer) Nordhaus-Gaddum results for restrained domination and total restrained domination in graphs, Discrete Mathematics 308 (2008) 1080 – 1087.
  61. (with E. Jonck and L.R. Markus) A note on the weakly connected subdivision number of a graph, The Bulletin of the Institute of Combinatorics and its Applications 53 (2008) 99-107.
  62. (with M.A. Henning) Restrained domination excellent trees, to appear in Ars Combinatoria. 
  63. (with E. Jonck and C.J. Ras) L(d,1)-minimal trees, to appear in Discrete Mathematics.
  64. (with A.R. Plummer) A note on restrained domination in trees, to appear in Ars Combinatoria.
  65. (with A. R. Plummer) Restrained bondage in graphs, to appear in Discrete Mathematics.
  66. (with A.R. Plummer and H.M. Xing) On the domination number of hamiltonian graphs, to appear in Applied Mathematics Letters.

 

 

The following papers have been submitted for publication.

 

  1. (with R. Gera, N. Jafari Rad, E.J. Joubert and L. van der Merwe) Vertex and edge critical total restrained domination in graphs.
  2. (with E. Jonck and E.J. Joubert) Bounds on the total restrained domination number of a graph.
  3. (with E. Jonck and E.J. Joubert) An upper bound on the total restrained domination number of a tree.
  4. (with E. Jonck and C.J. Ras) $\lambda_{2,1}$-Minimal trees of maximum
    degree at most three.
  5. (with E. Jonck and C.J. Ras) A class of full (d,1)-colorable trees
  6. (with E. J. Joubert, E. Jonck and A. R. Plummer) Total restrained domination in unicyclic graphs.
  7. (with E. J. Joubert, M. Loizeaux, A. R. Plummer and L. van der Merwe) Restrained domination in unicyclic graphs.

Johannes H. Hattingh's HomePage

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