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.