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- W4385246801 abstract "Let $G$ be a multigraph and $L,:,E(G) to 2^mathbb{N}$ be a list assignment on the edges of $G$. Suppose additionally, for every vertex $x$, the edges incident to $x$ have at least $f(x)$ colors in common. We consider a variant of local edge-colorings wherein the color received by an edge $e$ must be contained in $L(e)$. The locality appears in the function $f$, i.e., $f(x)$ is some function of the local structure of $x$ in $G$. Such a notion is a natural generalization of traditional local edge-coloring. Our main results include sufficient conditions on the function $f$ to construct such colorings. As corollaries, we obtain local analogs of Vizing and Shannon's theorems, recovering a recent result of Conley, Greb'ik and Pikhurko." @default.
- W4385246801 created "2023-07-26" @default.
- W4385246801 creator A5047573205 @default.
- W4385246801 date "2023-07-22" @default.
- W4385246801 modified "2023-09-23" @default.
- W4385246801 title "Multigraph edge-coloring with local list sizes" @default.
- W4385246801 doi "https://doi.org/10.48550/arxiv.2307.12094" @default.
- W4385246801 hasPublicationYear "2023" @default.
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