On an upper bound of a graph's chromatic number, depending on the graph's degree and density

O. V. Borodin; A. V. Kostochka

doi:10.1016/0095-8956(77)90037-5

On an upper bound of a graph's chromatic number, depending on the graph's degree and density

O. V. Borodin
, A. V. Kostochka

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

Abstract

Grünbaum's conjecture on the existence of k-chromatic graphs of degree k and girth g for every k ≥ 3, g ≥ 3 is disproved. In particular, the bound obtained states that the chromatic number of a triangle-free graph does not exceed [ 3(σ + 2) 4], where σ is the graph's degree.

Original language	English (US)
Pages (from-to)	247-250
Number of pages	4
Journal	Journal of Combinatorial Theory, Series B
Volume	23
Issue number	2-3
DOIs	https://doi.org/10.1016/0095-8956(77)90037-5
State	Published - 1977
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/0095-8956(77)90037-5

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AB - Grünbaum's conjecture on the existence of k-chromatic graphs of degree k and girth g for every k ≥ 3, g ≥ 3 is disproved. In particular, the bound obtained states that the chromatic number of a triangle-free graph does not exceed [ 3(σ + 2) 4], where σ is the graph's degree.

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On an upper bound of a graph's chromatic number, depending on the graph's degree and density

Abstract

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