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Igor Fabrici and Frank Göring

Abstract

A unique-maximum k-coloring with respect to faces of a plane graph G is a coloring with colors 1, . . . , k so that, for each face of G, the maximum color occurs exactly once on the vertices of α. We prove that any plane graph is unique-maximum 3-colorable and has a proper unique-maximum coloring with 6 colors.

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Yury Metelsky, Kseniya Schemeleva and Frank Werner

Abstract

We characterize the class L32 of intersection graphs of hypergraphs with rank at most 3 and multiplicity at most 2 by means of a finite list of forbidden induced subgraphs in the class of threshold graphs. We also give an O(n)-time algorithm for the recognition of graphs from L32 in the class of threshold graphs, where n is the number of vertices of a tested graph.

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Michael A. Henning and Christian Löwenstein

: 10.1016/j.dam.2013.01.025 [4] B. Brešar, S. Klav҆žar und D. Rall, Domination game and an imagination strategy, SIAM J. Discrete Math. 24 (2010) 979-991. doi: 10.1137/100786800 [5] B. Brešar, S. Klavžar and D. Rall, Domination game played on trees and spanning subgraphs, Discrete Math. 313 (2013) 915-923. doi: 10.1016/j.disc.2013.01.014 [6] Cs. Bujtás, Domination game on trees without leaves at distance four, in: Proc. 8th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications, A. Frank, A. Recski, G

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Boštan Brešar, Paul Dorbec, Sandi Klavžar and Gašpar Košmrlj

: 10.1016/j.dam.2013.01.025 [4] B. Brešar, S. Klavžar, G. Košmrlj and D.F. Rall, Guarded subgraphs and the domi- nation game, Discrete Math. Theor. Comput. Sci. 17 (2015) 161-168. [5] B. Brešar, S. Klavžar and D.F. Rall, Domination game and an imagination strategy, SIAM J. Discrete Math. 24 (2010) 979-991. doi: 10.1137/100786800 ` [6] Cs. Bujtás, Domination game on trees without leaves at distance four, in: A. Frank, A. Recski and G. Wiener (Eds.), Proceedings of the 8th Japanese-Hungarian Sym- posium on Discrete

Open access

Csilla Bujtás, Sandi Klavžar and Gašper Košmrlj

. Klavžar and D.F. Rall, Domination game and an imagination strategy, SIAM J. Discrete Math. 24 (2010) 979-991. doi:10.1137/100786800 [5] R.C. Brigham, P.Z. Chinn and R.D. Dutton, Vertex domination-critical graphs, Networks 1 (1988) 173-179. doi:10.1002/net.3230180304 [6] Cs. Bujtás, Domination game on trees without leaves at distance four, in: Proceedings of the 8th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications, A. Frank, A. Recski, G. Wiener, Eds., June 4-7 (2013) Veszpr´em, Hungary, 73-78. [7