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Lisa Markus - Mathematics

Research

                       

Here's an almost up-to-date list of my publications. I have mostly worked in two areas: Cycles and Paths, and Domination.

 Published:

 1. Markus, Lisa R. Hamiltonian results in $Ksb {1,r}$-free graphs. Proceedings of the Twenty-fourth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1993). Congr. Numer. 98 (1993), 143--149.

 2. Gunther, G.; Hartnell, B.; Markus, L. R.; Rall, D. Graphs with unique minimum dominating sets. Proceedings of the Twenty-fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1994). Congr. Numer. 101 (1994), 55--63.

 3. Dunbar, J. E.; Markus, L. R.; Rall, D. F. Graphs with two sizes of minimal dominating sets. Proceedings of the Twenty-sixth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1995). Congr. Numer. 111 (1995), 115--128.

 4. Chen, Guantao; Markus, Lisa R.; Schelp, R. H. Vertex disjoint cycles for star-free graphs. Australas. J. Combin. 11 (1995), 157--167.

 5. Markus, Lisa R. Paths through specified vertices of star-free graphs. Proceedings of the Twenty-seventh Southeastern International Conference on Combinatorics, Graph Theory and Computing (Baton Rouge, LA, 1996). Congr. Numer. 121 (1996), 154--160.

 6. Markus, Lisa R.; Snevily, Hunter S. Disjoint cycles in star-free graphs. J. Graph Theory 21 (1996), no. 4, 425--430.

 7. Domke, G. S.; Dunbar, J. E.; Haynes, T. W.; Knisley, D. J.; Markus, L. R. Independence, domination and generalized maximum degree. Proceedings of the Twenty-eighth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1997). Congr. Numer. 125  (1997), 145--152.

 8. Domke, Gayla S.; Dunbar, Jean E.; Markus, Lisa R. Gallai-type theorems and domination parameters. 15th British Combinatorial Conference (Stirling, 1995). Discrete Math. 167/168 (1997), 237--248.

 9. Markus, Lisa; Rall, Douglas. On seed graphs with two components. Ars Combin. 49 (1998), 193--204.

 10. Domke, G. S.; Dunbar, J. E.; Haynes, T. W.; Knisley, D. J.; Markus, L. R. Independence, domination and uniform maximum degree,  Proceedings of the Eighth International Conference on Graph Theory, Combinatorics, Algorithms and Applications 1 (1998) 291-301

 11. Markus, L. R. Disjoint cycles in planar and triangle-free graphs. Papers in honour of Stephen T. Hedetniemi. J. Combin. Math. Combin. Comput. 31 (1999), 177--182.

12. Dunbar, J. E.; Hattingh, J. H.; Laskar, R. C.; Markus, L. R. Domination using induced cliques in graphs. Ars Combin. 52 (1999), 129--139.

13. Domke, Gayla S.; Hattingh, Johannes H.; Hedetniemi, Stephen T.; Laskar, Renu C.; Markus, Lisa R. Restrained domination in graphs. Discrete Math. 203 (1999), no. 1-3, 61--69.

14. Domke, Gayla S.; Hattingh, Johannes H.; Henning, Michael A.; Markus, Lisa R. Restrained domination in trees. Discrete Math. 211 (2000), no. 1-3, 1-9.

15. Dunbar, J. E.; Hoffman, D. G.; Laskar, R. C.; Markus, L. R. $alpha$-domination. Discrete Math. 211 (2000), no. 1-3, 11-26.

16. Domke, Gayla S.; Hattingh, Johannes H.; Markus, Lisa R. On the number of edges in a graph with given domination-type parameters. Papers in honour of Ernest J. Cockayne. J. Combin. Math. Combin. Comput. 33 (2000), 23-32.

17. Domke, Gayla S.; Hattingh, Johannes H.; Henning, Michael A.; Markus, Lisa R. Restrained domination in graphs with minimum degree two. J. Combin. Math. Combin. Comput. 35 (2000), 239-254.

18. Haynes, T.W.; Markus, L.R.; Generalized maximum degree. Utilitas Math. 59 (2001), 155-165.

19. Domke, Gayla S.; Hattingh, Johannes H.; Henning, Markus,Lisa R.; Ungerer, Elna; On parameters related to strong and weak domination in graphs Discrete Mathematics 258(2002), 1-11.

20. Domke, G. S.; Markus, L. R. Generalised independent minimum t-degree. Util. Math.  62  (2002), 71-81.

21. Domke, Gayla S.; Dunbar, Jean E.; Markus, Lisa R.; The inverse domination number of a graph. Ars Combinatoria 72 (2004), 149-160.

22. Broere, I.; Jonck, E.; Domke, G.; Markus, L. The induced path number of the complements of some graphs. Australasian Jounrnal of Combinatorics 33 (2005), 15-32.

23. Domke, Gayla S.; Hattingh, Johannes H.; Markus,Lisa R.; On weakly connected domination in graphs II. Discrete Mathematics 305 (2005), 112-122.

24. Dankelmann, P.; Day, D.; Hattingh, J.; Henning, M.; Markus, L.; Swart, H.; On equality in an upper bound for the restrained and total domination numbers of a graph. Discrete Mathematics 307 (2007), 2845-2852.

25. Hattingh, Johannes H.; Jonck, Elizabeth; Markus, Lisa R. A note on the weakly connected domination subdivision number of a graph.  Bulletin of the Institute of Combinatorics and its Applications 53  (2008), 99--107.

26. Hedetniemi, Sandra M.; Hedetniemi, Stephen T.; Laskar, Renu C.; Markus, Lisa R.; Slater, Peter J.; Disjoint Dominating Sets in Graphs.  Proceedings of the International Conference on Discrete Mathematics. Ramanujan Mathematics Society Lecture Notes Series Volume 7 (2008), 87 -- 100.

 

To Appear:

 In Preparation:

 Inverse domination in trees, with G.S. Domke and J.E. Dunbar. 

A note on equality in an upper bound for the connected domination number of a graph.

 

                                            

 

 

 

 

 



Contact
email icon Email: Lisa Markus - email is the BEST way to reach me

The links on the LEFT are for my current courses. Use these to get the syllabus and other information.

Mathematics

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Last Updated: 9/16/14