Rainbow copies of C4 in edge-colored hypercubes

József Balogh; Michelle Delcourt; Bernard Lidický; Cory Palmer

doi:10.1016/j.dam.2014.10.002

Rainbow copies of _C4 in edge-colored hypercubes

József Balogh, Michelle Delcourt, Bernard Lidický, Cory Palmer

Mathematics

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

2 Scopus citations

Abstract

For positive integers k and d such that 4≤k<d and k 5, we determine the maximum number of rainbow colored copies of _C4 in a k-edge-coloring of the d-dimensional hypercube _Qd. Interestingly, the k-edge-colorings of _Qd yielding the maximum number of rainbow copies of _C4 also have the property that every copy of _C4 which is not rainbow is monochromatic.

Original language	English
Pages (from-to)	35-37
Number of pages	3
Journal	Discrete Applied Mathematics
Volume	210
DOIs	https://doi.org/10.1016/j.dam.2014.10.002
State	Published - Sep 10 2016

Keywords

Edge-coloring
Hypercube
Rainbow

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10.1016/j.dam.2014.10.002

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title = "Rainbow copies of C4 in edge-colored hypercubes",

abstract = "For positive integers k and d such that 4≤kC4 in a k-edge-coloring of the d-dimensional hypercube Qd. Interestingly, the k-edge-colorings of Qd yielding the maximum number of rainbow copies of C4 also have the property that every copy of C4 which is not rainbow is monochromatic.",

keywords = "Edge-coloring, Hypercube, Rainbow",

author = "J{\'o}zsef Balogh and Michelle Delcourt and Bernard Lidick{\'y} and Cory Palmer",

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doi = "10.1016/j.dam.2014.10.002",

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AU - Balogh, József

AU - Delcourt, Michelle

AU - Lidický, Bernard

AU - Palmer, Cory

PY - 2016/9/10

Y1 - 2016/9/10

N2 - For positive integers k and d such that 4≤kC4 in a k-edge-coloring of the d-dimensional hypercube Qd. Interestingly, the k-edge-colorings of Qd yielding the maximum number of rainbow copies of C4 also have the property that every copy of C4 which is not rainbow is monochromatic.

AB - For positive integers k and d such that 4≤kC4 in a k-edge-coloring of the d-dimensional hypercube Qd. Interestingly, the k-edge-colorings of Qd yielding the maximum number of rainbow copies of C4 also have the property that every copy of C4 which is not rainbow is monochromatic.

KW - Edge-coloring

KW - Hypercube

KW - Rainbow

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U2 - 10.1016/j.dam.2014.10.002

DO - 10.1016/j.dam.2014.10.002

M3 - Article

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VL - 210

SP - 35

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JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Rainbow copies of _C4 in edge-colored hypercubes

Abstract

Keywords

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