A new tool for proving Vizing's Theorem

Alexandr Kostochka

doi:10.1016/j.disc.2014.02.021

A new tool for proving Vizing's Theorem

Alexandr Kostochka

Mathematics

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

Abstract

The known proofs of the famous theorem of Vizing on edge coloring of (multi)graphs are not long but sophisticated. The main goal of this note is to present an auxiliary (multi)digraph that simplifies and facilitates proofs of it. The secondary goal is to use the approach for proofs of Vizing's Adjacency Lemma and the Andersen-Goldberg Theorem.

Original language	English (US)
Pages (from-to)	1-3
Number of pages	3
Journal	Discrete Mathematics
Volume	326
Issue number	1
DOIs	https://doi.org/10.1016/j.disc.2014.02.021
State	Published - Jul 6 2014

Keywords

Adjacency Lemma
Critical graphs
Edge coloring

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Online availability

10.1016/j.disc.2014.02.021

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title = "A new tool for proving Vizing's Theorem",

abstract = "The known proofs of the famous theorem of Vizing on edge coloring of (multi)graphs are not long but sophisticated. The main goal of this note is to present an auxiliary (multi)digraph that simplifies and facilitates proofs of it. The secondary goal is to use the approach for proofs of Vizing's Adjacency Lemma and the Andersen-Goldberg Theorem.",

keywords = "Adjacency Lemma, Critical graphs, Edge coloring",

author = "Alexandr Kostochka",

note = "Funding Information: I thank Douglas West, Xuding Zhu and Leonid Mel{\textquoteright}nikov for helpful discussions. Research is supported in part by NSF grant DMS-1266016 . Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",

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N2 - The known proofs of the famous theorem of Vizing on edge coloring of (multi)graphs are not long but sophisticated. The main goal of this note is to present an auxiliary (multi)digraph that simplifies and facilitates proofs of it. The secondary goal is to use the approach for proofs of Vizing's Adjacency Lemma and the Andersen-Goldberg Theorem.

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KW - Adjacency Lemma

KW - Critical graphs

KW - Edge coloring

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A new tool for proving Vizing's Theorem

Abstract

Keywords

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