Distance Matching Extension in Cubic Bipartite Graphs

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

Research output: Contribution to journalArticlepeer-review

Abstract

A graph G is said to be distanced matchable if, for any matching M of G in which edges are pairwise at least distance d apart, there exists a perfect matching M of G which contains M. In this paper, we prove the following results: (i) if G is a cubic bipartite graph in which, for each e∈ E(G) , there exist two cycles C1, C2 of length at most d such that E(C1) ∩ E(C2) = { e} , then G is distance d- 1 matchable, and (ii) if G is a planar or projective planar cubic bipartite graph in which, for each e∈ E(G) , there exist two cycles C1, C2 of length at most 6 such that e∈ E(C1) ∩ E(C2) , then G is distance 6 matchable.

Original languageEnglish
JournalGraphs and Combinatorics
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • 05C10
  • 05C70
  • Cubic bipartite graphs
  • Distance restricted matching extension
  • Planar graphs
  • Projective planar graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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