Displaying similar documents to “The B-Domatic Number of a Graph”

A Note on Non-Dominating Set Partitions in Graphs

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)...

A ramsey-type theorem for multiple disjoint copies of induced subgraphs

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...