A fast algorithm for equitable coloring

Henry Kierstead; Alexandr V. Kostochka; Marcelo Mydlarz; Endre Szemerédi

doi:10.1007/s00493-010-2483-5

A fast algorithm for equitable coloring

Henry Kierstead, Alexandr V. Kostochka, Marcelo Mydlarz, Endre Szemerédi

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

55 Scopus citations

Abstract

A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most one. The celebrated Hajnal-Szemerédi Theorem states: For every positive integer r, every graph with maximum degree at most r has an equitable coloring with r+1 colors. We show that this coloring can be obtained in O(rn²) time, where n is the number of vertices.

Original language	English (US)
Pages (from-to)	217-224
Number of pages	8
Journal	Combinatorica
Volume	30
Issue number	2
DOIs	https://doi.org/10.1007/s00493-010-2483-5
State	Published - 2010

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Mathematics

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title = "A fast algorithm for equitable coloring",

abstract = "A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most one. The celebrated Hajnal-Szemer{\'e}di Theorem states: For every positive integer r, every graph with maximum degree at most r has an equitable coloring with r+1 colors. We show that this coloring can be obtained in O(rn2) time, where n is the number of vertices.",

author = "Henry Kierstead and Kostochka, {Alexandr V.} and Marcelo Mydlarz and Endre Szemer{\'e}di",

note = "Funding Information: * Research of this author is supported in part by the NSA grant MDA 904-03-1-0007. † Research of this author is supported in part by NSF grant DMS-06-50784 and by grant 06-01-00694 of the Russian Foundation for Basic Research. ‡ Research of this author is supported in part by NSF grant DMS-0902241.",

year = "2010",

doi = "10.1007/s00493-010-2483-5",

language = "English (US)",

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pages = "217--224",

journal = "Combinatorica",

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T1 - A fast algorithm for equitable coloring

AU - Kierstead, Henry

AU - Kostochka, Alexandr V.

AU - Mydlarz, Marcelo

AU - Szemerédi, Endre

N1 - Funding Information: * Research of this author is supported in part by the NSA grant MDA 904-03-1-0007. † Research of this author is supported in part by NSF grant DMS-06-50784 and by grant 06-01-00694 of the Russian Foundation for Basic Research. ‡ Research of this author is supported in part by NSF grant DMS-0902241.

PY - 2010

Y1 - 2010

N2 - A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most one. The celebrated Hajnal-Szemerédi Theorem states: For every positive integer r, every graph with maximum degree at most r has an equitable coloring with r+1 colors. We show that this coloring can be obtained in O(rn2) time, where n is the number of vertices.

AB - A proper vertex coloring of a graph is equitable if the sizes of color classes differ by at most one. The celebrated Hajnal-Szemerédi Theorem states: For every positive integer r, every graph with maximum degree at most r has an equitable coloring with r+1 colors. We show that this coloring can be obtained in O(rn2) time, where n is the number of vertices.

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JO - Combinatorica

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A fast algorithm for equitable coloring

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