Bad news for chordal partitions

Alex Scott, Paul Seymour, David R Wood

Research output: Contribution to journalArticleResearchpeer-review

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

Cite this

Scott, Alex ; Seymour, Paul ; Wood, David R. / Bad news for chordal partitions. In: Journal of Graph Theory. 2019 ; Vol. 90, No. 1. pp. 5-12.
@article{1c3167d4bb8e49cca3323dea8987c4bf,
title = "Bad news for chordal partitions",
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.",
keywords = "chordal partition, graph, Hadwiger's conjecture, minor, partition",
author = "Alex Scott and Paul Seymour and Wood, {David R}",
year = "2019",
month = "1",
day = "1",
doi = "10.1002/jgt.22363",
language = "English",
volume = "90",
pages = "5--12",
journal = "Journal of Graph Theory",
issn = "0364-9024",
publisher = "John Wiley & Sons",
number = "1",

}

Bad news for chordal partitions. / Scott, Alex; Seymour, Paul; Wood, David R.

In: Journal of Graph Theory, Vol. 90, No. 1, 01.01.2019, p. 5-12.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Bad news for chordal partitions

AU - Scott, Alex

AU - Seymour, Paul

AU - Wood, David R

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - chordal partition

KW - graph

KW - Hadwiger's conjecture

KW - minor

KW - partition

UR - http://www.scopus.com/inward/record.url?scp=85056389727&partnerID=8YFLogxK

U2 - 10.1002/jgt.22363

DO - 10.1002/jgt.22363

M3 - Article

VL - 90

SP - 5

EP - 12

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 1

ER -