The Matching Extendability of Optimal 1-Planar Graphs

Jun Fujisawa, Keita Segawa, Yusuke Suzuki

Research output: Contribution to journalArticle

Abstract

A graph G is said to be 1-planar if it can be drawn on the sphere or plane so that any edge of G has at most one crossing point with another edge. Moreover, G is called an optimal 1-planar graph if | E(G) | = 4 | V(G) | - 8. In this paper, we investigate the matching extendability of optimal 1-planar graphs. It is shown that every optimal 1-planar graph G of even order is 2-extendable unless G contains a 4-cycle C which separates the graph into two odd components. Moreover, for any 5-connected optimal 1-planar graph, we characterize a matching with three edges which is not extendable.

Original languageEnglish
Pages (from-to)1089-1099
Number of pages11
JournalGraphs and Combinatorics
Volume34
Issue number5
DOIs
Publication statusPublished - 2018 Sep 1

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Keywords

  • Extendability
  • Optimal 1-planar graph
  • Perfect matching

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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