Completing Partial Proper Colorings using Hall's Condition

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Completing Partial Proper Colorings using Hall's Condition

In the context of list-coloring the vertices of a graph, Hall’s condition is a generalization of Hall’s Marriage Theorem and is necessary (but not sufficient) for a graph to admit a proper list-coloring. The graph G with list assignment L satisfies Hall’s condition if for each subgraph H of G, the inequality |V (H)| 6∑σ∈C α(H(σ, L)) is satisfied, where C is the set of colors and α(H(σ, L)) is t...

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ژورنال

عنوان ژورنال: The Electronic Journal of Combinatorics

سال: 2015

ISSN: 1077-8926

DOI: 10.37236/4387