Coloring Graphs with Sparse Neighborhoods

Noga Alon; Michael Krivelevich; Benny Sudakov

doi:10.1006/jctb.1999.1910

Coloring Graphs with Sparse Neighborhoods

Noga Alon
, Michael Krivelevich
, Benny Sudakov

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

90 Scopus citations

Abstract

It is shown that the chromatic number of any graph with maximum degree d in which the number of edges in the induced subgraph on the set of all neighbors of any vertex does not exceed d²/f is at most O(d/logf). This is tight (up to a constant factor) for all admissible values of d and f.

Original language	English
Pages (from-to)	73-82
Number of pages	10
Journal	Journal of Combinatorial Theory. Series B
Volume	77
Issue number	1
DOIs	https://doi.org/10.1006/jctb.1999.1910
State	Published - 1 Sep 1999
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1006/jctb.1999.1910

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title = "Coloring Graphs with Sparse Neighborhoods",

abstract = "It is shown that the chromatic number of any graph with maximum degree d in which the number of edges in the induced subgraph on the set of all neighbors of any vertex does not exceed d2/f is at most O(d/logf). This is tight (up to a constant factor) for all admissible values of d and f.",

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AU - Krivelevich, Michael

AU - Sudakov, Benny

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N2 - It is shown that the chromatic number of any graph with maximum degree d in which the number of edges in the induced subgraph on the set of all neighbors of any vertex does not exceed d2/f is at most O(d/logf). This is tight (up to a constant factor) for all admissible values of d and f.

AB - It is shown that the chromatic number of any graph with maximum degree d in which the number of edges in the induced subgraph on the set of all neighbors of any vertex does not exceed d2/f is at most O(d/logf). This is tight (up to a constant factor) for all admissible values of d and f.

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U2 - 10.1006/jctb.1999.1910

DO - 10.1006/jctb.1999.1910

M3 - Article

AN - SCOPUS:0003151866

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JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

IS - 1

ER -

Coloring Graphs with Sparse Neighborhoods

Abstract

ASJC Scopus subject areas

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