PROF Michael A. Henning,   PROFESSOR

School of Mathematical Sciences, University of KwaZulu-Natal, Pietermaritzburg campus, Scottsville 3209, South Africa   

henning@ukzn.ac.za

 Office Tel:   (27) 33 2605624   
Office Fax:  (27) 33 2605648  
 


 

Henning's Picture RESEARCH INTERESTS:  My research interests are in the field of graph theory which is a major area of combinatorics. I have worked on several topics in graph theory such as average connectivity in digraphs, distance in graphs, domination theory in graphs, extremal graph theory, graph colourings, hamiltonicity, homogeneous embeddings of graphs, Ramsey theory, Steiner distance in graphs, and transversals in hypergraphs. My favourite topic is in the area of domination theory in graphs. My current research is on the interplay between total domination in graphs and transversals in hypergraphs (with Anders Yeo from Royal Holloway, University of London).  
 

EDITORIAL  BOARDS OF SCIENTIFIC JOURNALS:              
  • I served as managing editor of the international mathematical journal Utilitas Mathematica for six years (January 1997 to December 2002), and have  recently resumed this position from June 2007.

PROFESSIONAL  SOCIETIES:

  • Elected Fellow of the Institute of Combinatorics and its Applications in July 1997.

REFEREE FOR SCIENTIFIC  JOURNALS:

  • I frequently serve as a referee for journals, including Ars Combinatoria, The Australasian Journal of Combinatorics, Discrete Mathematics, Discrete Applied Mathematics, Discussiones Mathematicae Graph Theory, Electronic Journal of Combinatorics, Graphs and Combinatorics, Journal of Combinatorial Mathematics and Combinatorial Computing, Journal of Graph Theory, Quaestiones Mathematicae, SIAM Journal of Discrete Mathematics and Utilitas Mathematica.

 

DOCTORAL  STUDENTS:

  • Hiren Maharaj, Graph and Digraph Embedding Problems. Ph.D completed: March 1996.
  • Laura Harris, Aspects of Functional Variations of Domination in Graphs. (Co-supervisor: Dr J.H. Hattingh.) Ph.D completed: November, 2003.
  • Jakes Maritz, Stratification and Domination in Graphs. Ph.D completed: April 2006.

SELECTED  RECENT  PUBLICATIONS:    

  • M. A. Henning and A. Yeo, Total domination in 2-connected graphs and in graphs with no induced 6-cycles. To appear in Journal of Graph Theory.
  • M. A. Henning and A. Yeo, Hypergraphs with large transversal number and with edge sizes at least three. To appear in Journal of Graph Theory.
  • M. A. Henning and A. Yeo, Total domination in graphs with given girth. To appear in Graphs and Combinatorics.
  • M. A. Henning, Recent results on total domination in graphs: A survey. To appear in Discrete Mathematics.
  • P. Dorbec, M. A. Henning, and D. F. Rall, On the upper total domination number of Cartesian products of graphs. Journal of Combinatorial Optimization 16 (2008), 68--80.
  • O. Favaron and M. A. Henning, Bounds on total domination in claw-free cubic graphs. Discrete Mathematics 308 (2008), 3491--3507.
  • O. Favaron and M. A. Henning, Total domination in claw-free graphs with minimum degree two. Discrete Mathematics 308 (2008), 3213--3219.
  • B. Bresar, M. A. Henning, and D. F. Rall, Rainbow domination in graphs. Taiwanese Journal of Mathematics 12 (2008), 201--213.
  • M. A. Henning and A. Yeo, Tight lower bounds on the size of a matching in a regular graph. Graphs and Combinatorics  23 (2007), 647--657.
  • M. A. Henning and A. Yeo, A new upper bound on the total domination number of a graph. Electronic Journal of Combinatorics 14 (2007) #R65.
  • W. Goddard and M. A. Henning, Restricted domination parameters in graphs. Journal of Combinatorial Optimization 13 (2007), 353--363.
  • M. A. Henning, Graphs with large paired-domination number. Journal of Combinatorial Optimization 13 (2007), 61--78.
  • M. A. Henning and A. Yeo, Total domination and matching numbers in claw-free graphs. Electronic Journal of Combinatorics 13 (2006), #59.
  • M. A. Henning and M. D. Plummer, Vertices contained in all or in no minimum paired-dominating set of a tree. Journal of Combinatorial Optimization 10 (2005), 283--294.
  • M.A. Henning, A linear Vizing-like relation relating the size and total domination number of a graph. Journal of Graph Theory 49 (2005), 285--290.
  • M. A. Henning and D. F. Rall, On the total domination number of Cartesian products of graph. Graphs and Combinatorics 21 (2005), 63--69.
  • W. Goddard and M.A. Henning, Multiple Vertex Coverings by Cliques. Journal of Graph Theory 48 (2005), 157--167.
  • O. Favaron and M.A. Henning, Paired domination in claw-free cubic graphs. Graphs and Combinatorics 20 (2004), 447--456.
  • O. Favaron and M.A. Henning, Upper total domination in claw-free graphs. Journal of Graph Theory 44 (2003), 148--158.
  • T.W. Haynes, S.T. Hedetniemi, and M.A. Henning, Global defensive alliances in graphs. Electronic Journal of Combinatorics 10 (2003), #47.
  • M.A. Henning, Total domination excellent trees. Discrete Mathematics 263 (2003), 93--104.
  • M.A. Henning, Defending the Roman Empire from multiple attacks. Discrete Mathematics 271 (2003), 101--115.
  • T.W. Haynes and M.A. Henning, Changing and unchanging domination: a classification. Discrete Mathematics 272 (2003), 65--79.
  • W. Goddard and M.A. Henning, Domination in planar graphs with small diameter. Journal of Graph Theory 40 (2002), 1--25
  • T.W. Haynes, S.M. Hedetniemi, S.T. Hedetniemi, and M.A. Henning, Power domination in graphs applied to electrical power networks. SIAM Journal of Discrete Mathematics 15(4) (2002), 519--529.
  • M.A. Henning, Restricted domination in graphs. Discrete Mathematics 254 (2002), 175--189.
  • W. Goddard and M.A. Henning, Pancyclicity of the prism. Discrete Mathematics 234 (2001), 139--142.
  • M.A. Henning, On cliques and bicliques. Journal of Graph Theory 34(1) (2000), 60--66.
  • O. Favaron, M.A. Henning, C.M. Mynhardt, and J. Puech, Total domination in graphs with minimum degree three. Journal of Graph Theory 34(1) (2000), 9--19.
  • J.H. Hattingh and M.A. Henning, Characterisations of trees with equal domination parameters. Journal of Graph Theory 34(2) (2000), 142--153
  • M.A. Henning, Graphs with large total domination number. Journal of Graph Theory 35(1) (2000), 21--45.
  • W. Goddard, M.A. Henning, and H. Maharaj, Homogeneous embeddings of cycles in graphs. Graphs and Combinatorics 15 (1999), 159--173.
  • M.A. Henning and H.R. Hind, Strict majority functions in graphs. Journal of Graph Theory 28 (1998), 49--56.
  • R.C. Entringer, W. Goddard, and M.A. Henning, A note on cliques and independent sets. Journal of Graph Theory 24 (1997), 21--23.

CHAPTERS IN BOOKS:

  • T.W. Haynes, and M.A. Henning, Domination in Graphs, 889-909. Handbook of Graph Theory ed. J.L. Gross and J. Yellen. CRC Press, December 2003, 1,176 pp. ISBN: 1584880922.
  • M.A. Henning, Dominating functions in graphs. Domination in Graphs: Advanced Topics, T.W. Haynes, S.T. Hedetniemi, and P.J. Slater (eds), Marcel Dekker, Inc. New York, 1998, 31--62.
  • M.A. Henning, Distance domination in graphs. Domination in Graphs: Advanced Topics, T.W. Haynes, S.T. Hedetniemi, and P.J. Slater (eds), Marcel Dekker, Inc. New York, 1998, 335--365.