Sum List Coloring Block Graphs

A graph is f-choosable if for every collection of lists with list sizes specified by f there is a proper coloring using colors from the lists. We characterize f-choosable functions for block graphs (graphs in which each block is a clique, including trees and line graphs of trees). The sum choice num...

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Bibliographic Details
Published inGraphs and combinatorics Vol. 20; no. 4; pp. 499 - 506
Main Author Isaak, Garth
Format Journal Article
LanguageEnglish
Published Tokyo Springer Nature B.V 01.11.2004
Subjects
Graph algorithms
Graph representations
Graph theory
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Summary:A graph is f-choosable if for every collection of lists with list sizes specified by f there is a proper coloring using colors from the lists. We characterize f-choosable functions for block graphs (graphs in which each block is a clique, including trees and line graphs of trees). The sum choice number is the minimum over all choosable functions f of the sum of the sizes in f. The sum choice number of any graph is at most the number of vertices plus the number of edges. We show that this bound is tight for block graphs. [PUBLICATION ABSTRACT]
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-004-0564-1