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Sum List Coloring Graphs

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Abstract

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 ∈ 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 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 K2, n , and we show that every tree on n vertices can be obtained from K n by consecutively deleting single edges where all intermediate graphs are sc-greedy.

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Madison, WI, 53706, USA

    Adam Berliner, Ulrike Bostelmann, Richard A. Brualdi & Louis Deaett

Authors
  1. Adam Berliner
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  2. Ulrike Bostelmann
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  3. Richard A. Brualdi
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  4. Louis Deaett
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Correspondence to Adam Berliner.

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Berliner, A., Bostelmann, U., Brualdi, R. et al. Sum List Coloring Graphs. Graphs and Combinatorics 22, 173–183 (2006). https://doi.org/10.1007/s00373-005-0645-9

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  • DOI: https://doi.org/10.1007/s00373-005-0645-9

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