Distance matching extension and local structure of graphs

R. E.L. Aldred, Jun Fujisawa, Akira Saito

Research output: Contribution to journalArticle

Abstract

A matching (Formula presented.) in a graph (Formula presented.) is said to be extendable if there exists a perfect matching of (Formula presented.) containing (Formula presented.). Also, (Formula presented.) is said to be a distance (Formula presented.) matching if the shortest distance between a pair of edges in (Formula presented.) is at least (Formula presented.). A graph (Formula presented.) is distance (Formula presented.) matchable if every distance (Formula presented.) matching is extendable in (Formula presented.), regardless of its size. In this paper, we study the class of distance (Formula presented.) matchable graphs. In particular, we prove that for every integer (Formula presented.) with (Formula presented.), there exists a positive integer (Formula presented.) such that every connected, locally (Formula presented.) -connected (Formula presented.) -free graph of even order is distance (Formula presented.) matchable. We also prove that every connected, locally (Formula presented.) -connected (Formula presented.) -free graph of even order is distance (Formula presented.) matchable. Furthermore, we make more detailed analysis of (Formula presented.) -free graphs and study their distance matching extension properties.

Original languageEnglish
Pages (from-to)5-20
Number of pages16
JournalJournal of Graph Theory
Volume93
Issue number1
DOIs
Publication statusPublished - 2020 Jan 1

Keywords

  • distance restricted matching extension
  • local connectivity
  • star-free

ASJC Scopus subject areas

  • Geometry and Topology

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