Note on highly connected monochromatic subgraphs in 2-colored complete graphs.
Fujita, Shinya, Magnant, Colton (2011)
The Electronic Journal of Combinatorics [electronic only]
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Fujita, Shinya, Magnant, Colton (2011)
The Electronic Journal of Combinatorics [electronic only]
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Caro, Yair, Lev, Arie, Roditty, Yehuda, Tuza, Zsolt, Yuster, Raphael (2008)
The Electronic Journal of Combinatorics [electronic only]
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Wang, Ping, Xu, Baoguang, Wang, Jianfang (2003)
The Electronic Journal of Combinatorics [electronic only]
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Zsolt Tuza (1989)
Acta Universitatis Carolinae. Mathematica et Physica
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Rackham, Tom (2009)
The Electronic Journal of Combinatorics [electronic only]
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Seyed Sheikholeslami (2010)
Open Mathematics
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A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ t(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the total domination number. Karami, Khoeilar, Sheikholeslami and Khodkar,...
Xueliang Li, Mengmeng Liu, Ingo Schiermeyer (2013)
Discussiones Mathematicae Graph Theory
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An edge-colored graph G is rainbow connected, if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this paper we show that rc(G) ≤ 3 if |E(G)| ≥ [...] + 2, and rc(G) ≤ 4 if |E(G)| ≥ [...] + 3. These bounds are sharp.
Bohdan Zelinka (1988)
Mathematica Slovaca
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