A condition for assured 3-face-colorability of infinite plane graphs with a given spanning tree

Eli Berger, Yanay Soker

Research output: Contribution to journalArticlepeer-review

Abstract

Given an infinite leafless tree drawn on the plane, we ask whether or not one can add edges between the vertices of the tree obtaining a non-3-face-colorable graph. We formulate a condition conjectured to be necessary and sufficient for this to be possible. We prove that this condition is indeed necessary and sufficient for trees with maximal degree 3, and that it is sufficient for general trees. In particular, we prove that every infinite plane graph with a spanning binary tree is 3-face-colorable.

Original languageEnglish
Pages (from-to)2919-2924
Number of pages6
JournalDiscrete Mathematics
Volume341
Issue number10
DOIs
StatePublished - Oct 2018

Bibliographical note

Funding Information:
The research of the first author is partially supported by the United States–Israel Binational Science Foundation grants 2012031 and 2016077 and by Israel Science Foundation grants 1581/12 and 936/16 . The research was initiated as a part of the Mentoring Program of Henrietta Szold Institute.

Publisher Copyright:
© 2018

Keywords

  • 05C10
  • 3-coloring
  • Planar graphs
  • Spanning trees

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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