Edge Kempe equivalence of regular graph covers

Nir Lazarovich; Arie Levit

doi:10.1002/jgt.22500

Edge Kempe equivalence of regular graph covers

Nir Lazarovich, Arie Levit

Mathematics

Technion - Israel Institute of Technology

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

Abstract

Let G be a finite d -regular graph with a proper edge coloring. An edge Kempe switch is a new proper edge coloring of G obtained by switching the two colors along some bichromatic cycle. We prove that any other edge coloring can be obtained by performing finitely many edge Kempe switches, provided that G is replaced with a suitable finite covering graph. The required covering degree is bounded above by a constant depending only on d.

Original language	English
Pages (from-to)	553-559
Number of pages	7
Journal	Journal of Graph Theory
Volume	93
Issue number	4
DOIs	https://doi.org/10.1002/jgt.22500
State	Published - 1 Apr 2020

Keywords

edge Kempe moves
graph coloring
graph covers
uniform tree lattices

All Science Journal Classification (ASJC) codes

Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1002/jgt.22500

Cite this

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abstract = "Let G be a finite d -regular graph with a proper edge coloring. An edge Kempe switch is a new proper edge coloring of G obtained by switching the two colors along some bichromatic cycle. We prove that any other edge coloring can be obtained by performing finitely many edge Kempe switches, provided that G is replaced with a suitable finite covering graph. The required covering degree is bounded above by a constant depending only on d.",

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AB - Let G be a finite d -regular graph with a proper edge coloring. An edge Kempe switch is a new proper edge coloring of G obtained by switching the two colors along some bichromatic cycle. We prove that any other edge coloring can be obtained by performing finitely many edge Kempe switches, provided that G is replaced with a suitable finite covering graph. The required covering degree is bounded above by a constant depending only on d.

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KW - graph coloring

KW - graph covers

KW - uniform tree lattices

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Edge Kempe equivalence of regular graph covers

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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