Degree conditions of nearly induced matching extendable graphs

Authors

  • Longshu Wu China Jiliang University
  • Qin Wang China Jiliang University

DOI:

https://doi.org/10.11575/cdm.v16i3.69926

Abstract

A graph G is induced matching extendable (shortly, IM-extendable) if every induced matching of G is included in a perfect matching of G. The IM-extendable graph was first introduced by Yuan. A graph G is nearly IM-extendable if GK1 is IM-extendable. We show in this paper that: (1) Let G be a graph with 2n1 vertices, where n2. If for each pair of nonadjacent vertices u and v in G, d(u)+d(v)24n/33, then G is nearly IM-extendable. (2) Let G be a claw-free graph with 2n1 vertices, where n2. If for each pair of nonadjacent vertices u and v in G, d(u)+d(v)2n1, then G is nearly IM-extendable. Minimum degree conditions of nearly IM-extendable graphs and nearly IM-extendable claw-free graphs are also obtained in this paper. It is also shown that all these results are best possible.

Author Biography

Longshu Wu, China Jiliang University

College of Sciences

Associate Professor

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Published

2021-12-31

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Section

Articles