ArticleOriginal scientific text

Title

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

Authors 1, 2, 2, 2

Affiliations

  1. Univ Paris-Sud, LRI, UMR 8623, Orsay, F-91405, France, CNRS, Orsay, F-91405
  2. Department of Mathematics, Azarbaijan University of Tarbiat Moallem, Tabriz, I.R. Iran

Abstract

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 sdγ(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, sdγ(G)γ(G)+1. In this paper we use matchings to prove this conjecture for graphs with at most three induced 4-cycles through each vertex.

Keywords

matching, barrier, total domination number, total domination subdivision number

Bibliography

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Pages:
611-618
Main language of publication
English
Received
2009-09-24
Accepted
2010-01-07
Published
2010
Exact and natural sciences