Abstract.
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.
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Acknowledgments. Partially supported by a grant from the Reidler Foundation. The author would like to thank an anonymous referee for useful comments.
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Isaak, G. Sum List Coloring Block Graphs. Graphs and Combinatorics 20, 499–506 (2004). https://doi.org/10.1007/s00373-004-0564-1
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DOI: https://doi.org/10.1007/s00373-004-0564-1