Home Page of Doug Rall
DOUG RALL'S home page


Professor Emeritus
Department of Mathematics
Furman University
Greenville, SC 29613
e-mail: doug dot rall at furman dot edu

Department of Mathematics Homepage
Furman University Homepage

Research and Scholarship

Book on the Cartesian Product of Graphs

Domination Games Played on Graphs

Ph. D. Students

Kirsti (Wash) Kuenzel

Jason Hedetniemi

Recent Publications

[98] B. Bresar, K. Kuenzel and D.F. Rall, Domination in digraphs and their direct and Cartesian products, Journal of Graph Theory, 99: 359--377 (2022) (DOI:10.1002/jgt.22744) [pdf] .

[97] B. L. Harnell and D. F. Rall, On graphs having one size of maximal open packings, Indian Journal of Discrete Mathematics 6(1): 1--14 (2021) [pdf] .

[96] S. Klavzar, D. F. Rall and I. G. Yero, General d-position sets, Ars Mathematica Contemporanea, 21, No. 1: 1--12 (P1.03)(2021) (DOI:10.26493/1855-3974.2384.77d) [pdf] .

[95] B. Bresar, J. Ferme, S. Klavzar and D. F. Rall, A survey on packing colorings, Discussiones Mathematicae Graph Theory, 40(4) (2020) 923--970 (DOI:10.7151/dmgt.2320).

[94] S. Anderson, K. Kuenzel and D. F. Rall, On well-dominated graphs, Graphs and Combinatorics 37(1): 151--165 (2021) (DOI: 10.1007/s00373-020-02235-z) [pdf] .

[93] M. A. Henning and D. F. Rall, The enclaveless competition game, Ars Mathematica Contemporanea, 20, No. 1:129--142 (2021). (DOI :10.26493/1855-3974.2227.e1a) [pdf] .

[92] B. Bresar, K. Kuenzel and D.F. Rall, Graphs with a unique maximum open packing, Indian Journal of Discrete Matheamtics, 5(1) (2019) 37--55 [pdf] .

[91] K. Kuenzel and D.F. Rall, On well-covered direct products, Discussiones Mathematicae Graph Theory, 42(2): 627--640 (2022) (DOI :10.7151/dmgt.2296) [pdf] .

[90] B. Bresar, B.L. Hartnell, M. A. Henning, K. Kuenzel and D.F. Rall, A new framework to approach Vizing's conjecture, Discussiones Mathematicae Graph Theory, 41(3): 749--763 (2021) (DOI :10.7151/dmgt.2293) [pdf] .

[89] S. Klavzar and D.F. Rall, Packing chromatic vertex-critical graphs, Discrete Mathematics and Theoretical Computer Science, 21(3), Paper #8, 18(2019) [pdf] .

[88] S. Klavzar and D.F. Rall, Domination game and minimal edge cuts, Discrete Mathematics, 342 (2019) 951-958 (DOI: 10.1016/j.disc.2018.12.001) [pdf] .

[87] B.L. Hartnell, D.F. Rall and Kirsti Wash, On well-covered Cartesian products, Graphs and Combinatorics, 34 (2018) 1259-1268 (DOI :10.1007/s00373-018-1943-3) Full-text View-only [pdf] .

[86] T.K. Sumenjak, D.F. Rall and A. Tepeh, On k-rainbow independent domination in graphs, Applied Mathematics and Computation, 333 (2018) 353-361 (DOI: 10.1016/j.amc.2018.03.013). [pdf]

[85] M. Henning, S. Klavzar and D.F. Rall, Game total domination critical graphs, Discrete Applied Mathematics, 250 (2018) 28-37 (DOI: 10.1016/j.dam.2018.04.014) . [pdf]

[84] B. Bresar, S. Klavzar, D.F. Rall and K. Wash, Packing chromatic number versus chromatic and clique number, Aequationes Mathematicae, 92 (2018) 497-513 (doi.org/10.1007/s00010-017-0520-9) [pdf] .

[83] D.F. Rall and Kirsti Wash, On minimum identifying codes in some Cartesian product graphs, Graphs and Combinatorics, 33 (2017) 1037-1053 (DOI 10.1007/s00373-017-1813-4) [pdf] .

[82] M. Henning and D.F. Rall, Trees with equal total domination and game total domination numbers, Discrete Applied Mathematics, 226 (2017) 58-70 (DOI:10.1016/j.dam.2017.03.012) [pdf] .

[81] M. Henning, S. Klavzar and D.F. Rall, The 4/5 upper bound on the game total domination number, Combinatorica, 37 (2017) 223-251 (DOI 10.1007/s00493-015-3316-3) Full-text View-only [pdf] .

[80] B. Bresar, B.L. Hartnell and D.F. Rall, Uniformly dissociated graphs, Ars Mathematica Contemporanea, 13 (2017) 293-306 [pdf] . (DOI 10.26493/1855-3974.1013.46a)

[79] B. Bresar, S. Klavzar, D.F. Rall and K. Wash, Packing chromatic number, (1,1,2,2)-colorings, and characterizing the Petersen graph, Aequationes Mathematicae, 91 (2017) 169-184 (DOI 10.1007/s00010-016-0461-8) [pdf] .

[78] B. Bresar, S. Klavzar, D.F. Rall and K. Wash, Packing chromatic number under local changes in a graph, Discrete Mathematics, 340 (2017) 1110-1115 (DOI:10.1016/j.disc.2016.09.030) [pdf] .

[77] T.K. Sumenjak, I. Peterin, D.F. Rall and A. Tepeh, Partitioning the vertex set of $G$ to make $G \Box H$ an efficient open domination graph, Discrete Mathematics and Theoretical Computer Science , 18:3 #10 (2016) 1-15 [pdf] .

[76] M. Henning and D.F. Rall, Progress towards the total domination game 3/4-conjecture, Discrete Mathematics, 339 (2016) 2620-2627 (DOI:10.1016/j.disc.2016.05.014) [pdf] .

[75] B. Bresar, M. Henning and D.F. Rall, Total dominating sequences in graphs, Discrete Mathematics, 339 (2016) 1665-1676 (DOI:10.1016/j.disc.2016.01.017) [pdf] .

[74] B. Bresar, S. Klavzar and D.F. Rall, Packing chromatic number of base-3 Sierpinski graphs, Graphs and Combinatorics, 32 (2016) 1313-1327 (DOI:10.1007/s00373-015-1647-x) Full-text View-only [pdf] .

[73] B. Bresar, S. Klavzar. G. Kosmrlj and D.F. Rall, Guarded subgraphs and the domination game, Discrete Mathematics and Theoretical Computer Science, 17:1 (2015) 161-168 [pdf] .

[72] B. Bresar and D.F. Rall, On Cartesian products having a minimum dominating set that is a box or a stairway, Graphs and Combinatorics, 31 (2015) 1263-1270 (DOI:10.1007/s00373-014-1486-1) [pdf] .

[71] B. Bresar, T. Gologranc, M. Milanic, D.F. Rall and R. Rizzi, Dominating sequences in graphs, Discrete Mathematics, 336 (2014) 22-36 (DOI: 10.1016/j.disc.2014.07.016). [pdf] .

[70] M. Henning, S. Klavzar and D.F. Rall, Total version of the domination game, Graphs and Combinatorics, 31 (2015) 1453-1462 (DOI 10.1007/s00373-014-1470-9) [pdf] .

[69] W. Desormeaux, M. Henning, D.F. Rall and A. Yeo, Relating the annihilation number and the 2-domination number of a tree, Discrete Mathematics, 319C (2014) 15-23 (DOI: 10.1016/j.disc.2013.11.020). [pdf] .

[68] D.F. Rall and Kirsti Wash, Identifying codes of the direct product of two cliques, European Journal of Combinatorics, 36 (2014) 159-171 (DOI: 10.1016/j.ejc.2013.07.002). [pdf] .

[67] B. Hartnell and D.F. Rall, On the Cartesian product of non well-covered graphs, The Electronic Journal of Combinatorics, 20(2) #P21 (2013) 1-4 [pdf] .

[66] T.K. Sumenjak, D.F. Rall and A. Tepeh, Rainbow domination in the lexicographic product of graphs, Discrete Applied Mathematics, 161 (2013) 2133-2141 (DOI: 10.1016/j.dam.2013.03.011). [pdf]

[65] B. Bresar, S. Klavzar. G. Kosmrlj and D.F. Rall, Domination game: extremal families of graphs for the 3/5-conjectures, Discrete Applied Mathematics, 161 (2013) 1308-1316 (DOI: 10.1016/j.dam.2013.01.025). [pdf]

[64] B. Bresar, S. Klavzar and D.F. Rall, Domination game played on trees and spanning subgraphs, Discrete Mathematics, 313 (2013) 915-923 (DOI: 10.1016/j.disc.2013.01.014) . [pdf]

[63] M. Henning and D.F. Rall, On graphs with disjoint dominating and 2-dominating sets, Discussiones Mathematicae Graph Theory, 33 (2013) 139-146. [pdf]

[62] B. Hartnell and D.F. Rall, On graphs having maximal independent sets of exactly t distinct cardinalities, Graphs and Combinatorics 29(3) (2013) 519-525 (DOI: 10.1007/s00373-012-1132-8) . [pdf]

[61] B. Bresar, P. Dorbec, W. Goddard, B. Hartnell, M. Henning, S. Klavzar, and D. F. Rall, Vizing's Conjecture: A Survey and Recent Results, Journal of Graph Theory, 69 (2012) 46-76 (DOI: 10.1002/jgt.20565) . [pdf]

[60] B. Bresar, S. Klavzar and D.F. Rall, Domination game and an imagination strategy, SIAM Journal on Discrete Mathematics, 24 (2010) 979-991. [pdf]

[59] A. Finbow and D.F. Rall, On the packing chromatic number of some lattices, Discrete Applied Mathematics, 158 (2010) 1224-1228. [pdf]

[58] R. Gallant, G. Gunther, B. Hartnell and D.F. Rall, Limited packings in graphs, Discrete Applied Mathematics, 158 (2010) 1357-1364. [pdf]

Earlier Papers

Several Connections to the Mathematical World

Electronic Journal of Combinatorics
AMS e-MATH
NSF Mathematical Sciences Institutes


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