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Sum List Coloring Graphs
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Journal Article
Sum List Coloring Graphs
2006
Overview
Let G=(V,E) be a graph with n vertices and e edges. The sum choice number of G is the smallest integer p such that there exist list sizes (f(v):v belongs to V) whose sum is p for which G has a proper coloring no matter which color lists of size f(v) are assigned to the vertices v. The sum choice number is bounded above by n+e. If the sum choice number of G equals n+e, then G is sum choice greedy. Complete graphs K[subscript n] are sum choice greedy as are trees. Based on a simple, but powerful, lemma we show that a graph each of whose blocks is sum choice greedy is also sum choice greedy. We also determine the sum choice number of K[subscript 2,n], and we show that every tree on n vertices can be obtained from K[subscript n] by consecutively deleting single edges where all intermediate graphs are sc-greedy. [PUBLICATION ABSTRACT]
Publisher
Springer Nature B.V
Subject
