Subgraphs with a Large Cochromatic Number

Noga Alon; Michael Krivelevich; Benny Sudakov

doi:10.1002/(SICI)1097-0118(199708)25:4<295::AID-JGT7>3.0.CO;2-F

Subgraphs with a Large Cochromatic Number

Noga Alon
, Michael Krivelevich
, Benny Sudakov

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

8 Scopus citations

Abstract

The cochromatic number of a graph G = (V, E) is the smallest number of parts in a partition of V in which each part is either an independent set or induces a complete subgraph. We show that if the chromatic number of G is n, then G contains a subgraph with cochromatic number at least Ω(n/lnn). This is tight, up to the constant factor, and settles a problem of Erdos and Gimbel.

Original language	English (US)
Pages (from-to)	295-297
Number of pages	3
Journal	Journal of Graph Theory
Volume	25
Issue number	4
DOIs	https://doi.org/10.1002/(SICI)1097-0118(199708)25:4<295::AID-JGT7>3.0.CO;2-F
State	Published - Aug 1997
Externally published	Yes

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Chromatic number
Graph coloring
Ramsey theory

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10.1002/(SICI)1097-0118(199708)25:4<295::AID-JGT7>3.0.CO;2-F

Cite this

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keywords = "Chromatic number, Graph coloring, Ramsey theory",

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T1 - Subgraphs with a Large Cochromatic Number

AU - Alon, Noga

AU - Krivelevich, Michael

AU - Sudakov, Benny

PY - 1997/8

Y1 - 1997/8

N2 - The cochromatic number of a graph G = (V, E) is the smallest number of parts in a partition of V in which each part is either an independent set or induces a complete subgraph. We show that if the chromatic number of G is n, then G contains a subgraph with cochromatic number at least Ω(n/lnn). This is tight, up to the constant factor, and settles a problem of Erdos and Gimbel.

AB - The cochromatic number of a graph G = (V, E) is the smallest number of parts in a partition of V in which each part is either an independent set or induces a complete subgraph. We show that if the chromatic number of G is n, then G contains a subgraph with cochromatic number at least Ω(n/lnn). This is tight, up to the constant factor, and settles a problem of Erdos and Gimbel.

KW - Chromatic number

KW - Graph coloring

KW - Ramsey theory

UR - https://www.scopus.com/pages/publications/0031475889

UR - https://www.scopus.com/pages/publications/0031475889#tab=citedBy

U2 - 10.1002/(SICI)1097-0118(199708)25:4<295::AID-JGT7>3.0.CO;2-F

DO - 10.1002/(SICI)1097-0118(199708)25:4<295::AID-JGT7>3.0.CO;2-F

M3 - Article

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SN - 0364-9024

VL - 25

SP - 295

EP - 297

JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 4

ER -

Subgraphs with a Large Cochromatic Number

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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