TY - JOUR

T1 - A pair of forbidden subgraphs and perfect matchings

AU - Fujita, Shinya

AU - Kawarabayashi, Ken ichi

AU - Leonardo Lucchesi, Claudio

AU - Ota, Katsuhiro

AU - Plummer, Michael D.

AU - Saito, Akira

N1 - Funding Information:
1 Partially supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research, by Sumitomo Foundation and by Inoue Research Award for Young Scientists. 2Supported by a grant from CNPq and by Pronex/CNPq 664107/1997-4. 3 Partially supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C),13640138, 2002 and 15540140, 2003–2004.

PY - 2006/5

Y1 - 2006/5

N2 - In this paper, we study the relationship between forbidden subgraphs and the existence of a matching. Let H be a set of connected graphs, each of which has three or more vertices. A graph G is said to be H-free if no graph in H is an induced subgraph of G. We completely characterize the set H such that every connected H-free graph of sufficiently large even order has a perfect matching in the following cases. (1)Every graph in H is triangle-free.(2) H consists of two graphs (i.e. a pair of forbidden subgraphs).A matching M in a graph of odd order is said to be a near-perfect matching if every vertex of G but one is incident with an edge of M. We also characterize H such that every H-free graph of sufficiently large odd order has a near-perfect matching in the above cases.

AB - In this paper, we study the relationship between forbidden subgraphs and the existence of a matching. Let H be a set of connected graphs, each of which has three or more vertices. A graph G is said to be H-free if no graph in H is an induced subgraph of G. We completely characterize the set H such that every connected H-free graph of sufficiently large even order has a perfect matching in the following cases. (1)Every graph in H is triangle-free.(2) H consists of two graphs (i.e. a pair of forbidden subgraphs).A matching M in a graph of odd order is said to be a near-perfect matching if every vertex of G but one is incident with an edge of M. We also characterize H such that every H-free graph of sufficiently large odd order has a near-perfect matching in the above cases.

KW - Forbidden subgraph

KW - Near-perfect matching

KW - Perfect matching

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U2 - 10.1016/j.jctb.2005.08.002

DO - 10.1016/j.jctb.2005.08.002

M3 - Article

AN - SCOPUS:33645931353

SN - 0095-8956

VL - 96

SP - 315

EP - 324

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

IS - 3

ER -