Bad news for chordal partitions

Alex Scott, Paul Seymour, David R Wood

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

Reed and Seymour [1998] asked whether every graph has a partition into induced connected nonempty bipartite subgraphs such that the quotient graph is chordal. If true, this would have significant ramifications for Hadwiger's Conjecture. We prove that the answer is “no.” In fact, we show that the answer is still “no” for several relaxations of the question.

Original languageEnglish
Pages (from-to)5-12
Number of pages8
JournalJournal of Graph Theory
Volume90
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • chordal partition
  • graph
  • Hadwiger's conjecture
  • minor
  • partition

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