On -ply domatic numbers of graphs
Bohdan Zelinka (1984)
Mathematica Slovaca
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Bohdan Zelinka (1984)
Mathematica Slovaca
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Igor Edmundovich Zverovich, Vadim E. Zverovich (1991)
Czechoslovak Mathematical Journal
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Gutman, Ivan (1989)
Publications de l'Institut Mathématique. Nouvelle Série
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Bohdan Zelinka (1981)
Časopis pro pěstování matematiky
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Wyatt J. Desormeaux, Teresa W. Haynes, Michael A. Henning (2016)
Discussiones Mathematicae Graph Theory
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A set S of vertices of a graph G is a dominating set if every vertex not in S is adjacent to a vertex of S and is a total dominating set if every vertex of G is adjacent to a vertex of S. The cardinality of a minimum dominating (total dominating) set of G is called the domination (total domination) number. A set that does not dominate (totally dominate) G is called a non-dominating (non-total dominating) set of G. A partition of the vertices of G into non-dominating (non-total dominating)...
Zelinka, Bohdan (1996)
Archivum Mathematicum
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Tomoki Nakamigawa (2014)
Discussiones Mathematicae Graph Theory
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Let k and ℓ be positive integers with ℓ ≤ k − 2. It is proved that there exists a positive integer c depending on k and ℓ such that every graph of order (2k−1−ℓ/k)n+c contains n vertex disjoint induced subgraphs, where these subgraphs are isomorphic to each other and they are isomorphic to one of four graphs: (1) a clique of order k, (2) an independent set of order k, (3) the join of a clique of order ℓ and an independent set of order k − ℓ, or (4) the union of an independent set of...