Local and global colorability of graphs

Noga Alon, Omri Ben-Eliezer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)428-442
Number of pages15
JournalDiscrete Mathematics
Volume339
Issue number2
DOIs
StatePublished - 6 Feb 2016

Funding

FundersFunder number
Israeli I-Core
USA-Israeli BSF2012/107
Israel Science Foundation620/13

    Keywords

    • 2-degeneracy
    • Local chromatic number
    • Local colorability

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