Abstract:Let F be a (possibly improper) edge-coloring of a graph G; a vertex coloring of G is adapted to F if no color appears at the same time on an edge and on its two endpoints. If for some integer k, a graph G is such that given any list assignment L to the vertices of G, with |L(v)| ≥ k for all v, and any edge-coloring F of G, G admits a coloring c adapted to F where c(v) ∈ L(v) for all v, then G is said to be adaptably k-choosable. A (k, d)-list assignment for a graph G is a map that assigns to each vertex v a li… Show more
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