Brooksʼ Theorem for generalized dart graphs

The well-known Brooksʼ Theorem says that each graph G of maximum degree k ⩾ 3 is k-colorable unless G = K k + 1 . We generalize this theorem by allowing higher degree vertices with prescribed types of neighborhood. ► Generalization of Brooks Theorem for ( k , s ) -dart graphs. ► Linear algorithm for...

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Bibliographic Details
Published inInformation processing letters Vol. 112; no. 5; pp. 200 - 204
Main Authors Kochol, Martin, Škrekovski, Riste
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 28.02.2012
Elsevier Sequoia S.A
Subjects
[formula omitted]-dart graph
[formula omitted]-diamond
Brooksʼ Theorem
Graph algorithms
Graph coloring
Graphs
Mathematical programming
NP-complete problem
Studies
Theorems
Graph algorithms
NP-complete problem
Brooksʼ Theorem
( k , s ) -dart graph
( k , s ) -diamond
Online AccessGet full text
ISSN0020-0190
1872-6119
DOI10.1016/j.ipl.2011.11.010

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Summary:The well-known Brooksʼ Theorem says that each graph G of maximum degree k ⩾ 3 is k-colorable unless G = K k + 1 . We generalize this theorem by allowing higher degree vertices with prescribed types of neighborhood. ► Generalization of Brooks Theorem for ( k , s ) -dart graphs. ► Linear algorithm for ( k + 1 ) -coloring of ( k , s ) -dart graphs with s not greater then k. ► NP-completeness for ( k + 1 ) -coloring of ( k , s ) -dart graphs with s greater then k.
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ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2011.11.010