Elsevier

Discrete Mathematics

Volume 146, Issues 1–3, 15 November 1995, Pages 11-18
Discrete Mathematics

Dominating cycles in bipartite biclaw-free graphs

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Abstract

Flandrin et al. (to appear) define a simple bipartite graph to be biclaw-free if it contains no induced subgraph isomorphic to H, where H could be obtained from two copies of K1,3 by adding an edge joining the two vertices of degree 3. They have shown that if G is a bipartite, balanced, biclaw-free connected graph of order at most 6δ–10, then G is hamiltonian. In this paper we show that if G is a bipartite, balanced, biclaw-free connected graph of order at most 8δ–69, where δ ⩾ 24, then every longest cycle in G is dominating, i.e., every edge has at least one end-vertex on the cycle.

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This work was done while the two authors were visiting the Mathematics Department of the Universidad Central de Venezuela.