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Matchings and total domination subdivision number in graphs with few induced 4-cycles

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Favaron O., Karami H., Khoeilar R., Sheikholeslami S.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 4

611-618

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 γₜ(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number $sd_{γₜ(G)}$ 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. Favaron, Karami, Khoeilar and Sheikholeslami (Journal of Combinatorial Optimization, to appear) conjectured that: For any connected graph G of order n ≥ 3, $sd_{γₜ(G)} ≤ γₜ(G)+1$. In this paper we use matchings to prove this conjecture for graphs with at most three induced 4-cycles through each vertex.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Favaron O.

1 Karami H.

1 Khoeilar R.

1 Sheikholeslami S.

1 2010

Wyniki wyszukiwania

Matchings and total domination subdivision number in graphs with few induced 4-cycles