A Ramsey-type result for the hypercube

Noga Alon; Radoš Radoičić; Benny Sudakov; Jan Vondrák

doi:10.1002/jgt.20181

A Ramsey-type result for the hypercube

Noga Alon
, Radoš Radoičić
, Benny Sudakov
, Jan Vondrák

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

24 Scopus citations

Abstract

We prove that for every fixed k and ℓ ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Q_n with k colors contains a monochromatic cycle of length 2ℓ. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, that is, have the property that for every k, any k-edge coloring of a sufficiently large Q_n contains a monochromatic copy of H.

Original language	English (US)
Pages (from-to)	196-208
Number of pages	13
Journal	Journal of Graph Theory
Volume	53
Issue number	3
DOIs	https://doi.org/10.1002/jgt.20181
State	Published - Nov 2006
Externally published	Yes

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Hypercube
Monochromatic cycles
Ramsey theory

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10.1002/jgt.20181

Cite this

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abstract = "We prove that for every fixed k and ℓ ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Qn with k colors contains a monochromatic cycle of length 2ℓ. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, that is, have the property that for every k, any k-edge coloring of a sufficiently large Qn contains a monochromatic copy of H.",

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AU - Alon, Noga

AU - Radoičić, Radoš

AU - Sudakov, Benny

AU - Vondrák, Jan

PY - 2006/11

Y1 - 2006/11

N2 - We prove that for every fixed k and ℓ ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Qn with k colors contains a monochromatic cycle of length 2ℓ. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, that is, have the property that for every k, any k-edge coloring of a sufficiently large Qn contains a monochromatic copy of H.

AB - We prove that for every fixed k and ℓ ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Qn with k colors contains a monochromatic cycle of length 2ℓ. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, that is, have the property that for every k, any k-edge coloring of a sufficiently large Qn contains a monochromatic copy of H.

KW - Hypercube

KW - Monochromatic cycles

KW - Ramsey theory

UR - https://www.scopus.com/pages/publications/33750471208

UR - https://www.scopus.com/pages/publications/33750471208#tab=citedBy

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JO - Journal of Graph Theory

JF - Journal of Graph Theory

IS - 3

ER -

A Ramsey-type result for the hypercube

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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