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

Mathematical Sciences

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

Funding

The first author’s research is partially supported by NSF CAREER Grant DMS-0745185 , Marie Curie FP7-PEOPLE-2012-IIF 327763 by the European Union and co-funded by the European Social Fund under the project “Telemedicine-focused research activities on the field of Mathematics, Informatics and Medical sciences” of project number “TÁMOP-4.2.2.A-11/1/KONV-2012-0073”. The second author’s research was supported by NSF Graduate Research Fellowship DGE 1144245 and DMS 0838434 EMSW21MCTP: Research Experience for Graduate Students. The third author’s research is partially supported by NSF Grant DMS-1266016 . The fourth author’s research was supported by Hungarian National Science Fund (OTKA), Grant NK 78439 .

Funders	Funder number
327763
DMS-0745185
European Commission
NK 78439
DMS-1266016, DGE 1144245, DMS 0838434

Keywords

Edge-coloring
Hypercube
Rainbow

Access to Document

10.1016/j.dam.2014.10.002

Cite this

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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.",

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AU - Lidický, Bernard

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