Independence number and disjoint theta 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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Justin Southey, Michael Henning (2010)
Open Mathematics
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A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a paired-dominating set of a graph is a dominating set such that the subgraph induced by the dominating set contains a perfect matching. In this paper, we show that no minimum degree is sufficient to guarantee the existence of a disjoint dominating set and a paired-dominating set. However, we prove that the vertex set of every cubic graph can be partitioned...
Chia, Gek Ling, Ho, Chee-Kit (2003)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Henning, Michael A., Yeo, Anders (2007)
The Electronic Journal of Combinatorics [electronic only]
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Henning, Michael A., Schiermeyer, Ingo, Yeo, Anders (2011)
The Electronic Journal of Combinatorics [electronic only]
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M.S.A. Bataineh, M.M.M. Jaradat, M.S. Bateeha (2014)
Discussiones Mathematicae Graph Theory
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For any two graphs F1 and F2, the graph Ramsey number r(F1, F2) is the smallest positive integer N with the property that every graph on at least N vertices contains F1 or its complement contains F2 as a subgraph. In this paper, we consider the Ramsey numbers for theta-complete graphs. We determine r(θn,Km) for m = 2, 3, 4 and n > m. More specifically, we establish that r(θn,Km) = (n − 1)(m − 1) + 1 for m = 3, 4 and n > m
Bohdan Zelinka (1986)
Czechoslovak Mathematical Journal
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Ralph J. Faudree, Cecil C. Rousseau, Richard H. Schelp, Seymour Schuster (1981)
Czechoslovak Mathematical Journal
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