TY - JOUR
T1 - Hadwiger's conjecture for degree sequences
AU - Chen, Guantao
AU - Ota, Katsuhiro
N1 - Publisher Copyright:
© 2015 Elsevier Inc.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2015/9/1
Y1 - 2015/9/1
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
UR - http://www.scopus.com/inward/record.url?scp=84930571254&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84930571254&partnerID=8YFLogxK
U2 - 10.1016/j.jctb.2015.03.006
DO - 10.1016/j.jctb.2015.03.006
M3 - Article
AN - SCOPUS:84930571254
VL - 114
SP - 247
EP - 249
JO - Journal of Combinatorial Theory. Series B
JF - Journal of Combinatorial Theory. Series B
SN - 0095-8956
ER -