Abstract.
We say that a graph G is quasi claw-free if every pair (a 1, a 2) of vertices at distance 2 satisfies {u∈N (a 1)∩N (a 2) | N[u]⊆N[a 1]∪N [a 2]}≠∅. A cycle C is m-dominating if every vertex of G is of distance at most m from C. We prove that if G is a κ-connected (κ≥2) quasi claw-free graph then either G has an m-dominating cycle or G has a set of at least κ+1 vertices such that the distance between every pair of them is at least 2m+3.
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Received: June 12, 1996 Revised: November 9, 1998
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Chen, C., Harkat-Benhamdine, A. & Li, H. Distance-Dominating Cycles in Quasi Claw-Free Graphs. Graphs Comb 15, 279–285 (1999). https://doi.org/10.1007/s003730050061
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DOI: https://doi.org/10.1007/s003730050061