Choosability of a weighted path and free-choosability of a cycle

Details Choosability of a weighted path and free-choosability of a cycle Choosability of a weighted path and free-choosability of a cycle

2010-05-31

arxiv.org/abs/1005.5602v3

Mathematics

Combinatorics

9 pages

Scientific paper

A graph $G$ with a list of colors $L(v)$ and weight $w(v)$ for each vertex $v$ is $(L,w)$-colorable if one can choose a subset of $w(v)$ colors from $L(v)$ for each vertex $v$, such that adjacent vertices receive disjoint color sets. In this paper, we give necessary and sufficient conditions for a weighted path to be $(L,w)$-colorable for some list assignments $L$. Furthermore, we solve the problem of the free-choosability of a cycle.

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