TY - JOUR

T1 - Local and global colorability of graphs

AU - Alon, Noga

AU - Ben-Eliezer, Omri

N1 - Publisher Copyright:
© 2015 Elsevier B.V.All rights reserved.

PY - 2016/2/6

Y1 - 2016/2/6

N2 - It is shown that for any fixed c3 and r, the maximum possible chromatic number of a graph on n vertices in which every subgraph of radius at most r is c-colorable is Θ(n1r+1): it is O((n/logn)1r+1) and Ω(n1r+1/logn). The proof is based on a careful analysis of the local and global colorability of random graphs and implies, in particular, that a random n-vertex graph with the right edge probability has typically a chromatic number as above and yet most balls of radius r in it are 2-degenerate.

AB - It is shown that for any fixed c3 and r, the maximum possible chromatic number of a graph on n vertices in which every subgraph of radius at most r is c-colorable is Θ(n1r+1): it is O((n/logn)1r+1) and Ω(n1r+1/logn). The proof is based on a careful analysis of the local and global colorability of random graphs and implies, in particular, that a random n-vertex graph with the right edge probability has typically a chromatic number as above and yet most balls of radius r in it are 2-degenerate.

KW - 2-degeneracy

KW - Local chromatic number

KW - Local colorability

UR - http://www.scopus.com/inward/record.url?scp=84943179136&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2015.09.006

DO - 10.1016/j.disc.2015.09.006

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AN - SCOPUS:84943179136

SN - 0012-365X

VL - 339

SP - 428

EP - 442

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 2

ER -