Hadwiger's conjecture for degree sequences

Guantao Chen; Katsuhiro Ota

doi:10.1016/j.jctb.2015.03.006

Hadwiger's conjecture for degree sequences

Guantao Chen, Katsuhiro Ota

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Hadwiger conjectured that every graph contains K_χ(G) as a minor, where χ(G) is the chromatic number of G. In 2005, Robertson made a weaker conjecture that for any graph G, there exists a graph H with the same degree sequence of G and containing K_χ(G) as a minor, which was confirmed by Dvořák and Mohar recently. In this note, we give a short proof of Robertson's Conjecture.

Original language	English
Pages (from-to)	247-249
Number of pages	3
Journal	Journal of Combinatorial Theory. Series B
Volume	114
DOIs	https://doi.org/10.1016/j.jctb.2015.03.006
Publication status	Published - 2015 Sept 1

Keywords

Chromatic numbers
Degree sequences
Graph minors
Hadwiger's conjecture

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jctb.2015.03.006

Cite this

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title = "Hadwiger's conjecture for degree sequences",

abstract = "Hadwiger conjectured that every graph contains Kχ(G) as a minor, where χ(G) is the chromatic number of G. In 2005, Robertson made a weaker conjecture that for any graph G, there exists a graph H with the same degree sequence of G and containing Kχ(G) as a minor, which was confirmed by Dvo{\v r}{\'a}k and Mohar recently. In this note, we give a short proof of Robertson's Conjecture.",

keywords = "Chromatic numbers, Degree sequences, Graph minors, Hadwiger's conjecture",

author = "Guantao Chen and Katsuhiro Ota",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2015",

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doi = "10.1016/j.jctb.2015.03.006",

language = "English",

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AU - Ota, Katsuhiro

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N2 - Hadwiger conjectured that every graph contains Kχ(G) as a minor, where χ(G) is the chromatic number of G. In 2005, Robertson made a weaker conjecture that for any graph G, there exists a graph H with the same degree sequence of G and containing Kχ(G) as a minor, which was confirmed by Dvořák and Mohar recently. In this note, we give a short proof of Robertson's Conjecture.

AB - Hadwiger conjectured that every graph contains Kχ(G) as a minor, where χ(G) is the chromatic number of G. In 2005, Robertson made a weaker conjecture that for any graph G, there exists a graph H with the same degree sequence of G and containing Kχ(G) as a minor, which was confirmed by Dvořák and Mohar recently. In this note, we give a short proof of Robertson's Conjecture.

KW - Chromatic numbers

KW - Degree sequences

KW - Graph minors

KW - Hadwiger's conjecture

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JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

ER -

Hadwiger's conjecture for degree sequences

Abstract

Keywords

ASJC Scopus subject areas

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