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- W4288242577 abstract "Let $chi'_subset(G)$ be the least number of colours necessary to properly colour the edges of a graph $G$ with minimum degree $deltageq 2$ so that the set of colours incident with any vertex is not contained in a set of colours incident to any its neighbour. We provide an infinite family of examples of graphs $G$ with $chi'_subset(G)geq (1+frac{1}{delta-1})Delta$, where $Delta$ is the maximum degree of $G$, and we conjecture that $chi'_subset(G)leq lceil(1+frac{1}{delta-1})Deltarceil$ for every connected graph with $deltageq 2$ which is not isomorphic to $C_5$. The equality here is attained e.g. for the family of complete bipartite graphs. Using a probabilistic argument we support this conjecture by proving that for any fixed $deltage2$, $chi'_subset(G) le (1+frac{4}{delta})Delta (1+o(1))$ (for $Deltatoinfty$), what implies that $chi'_subset(G) le (1+frac{4}{delta-1})Delta$ for $Delta$ large enough." @default.
- W4288242577 created "2022-07-28" @default.
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- W4288242577 date "2019-08-31" @default.
- W4288242577 modified "2023-10-17" @default.
- W4288242577 title "On inclusion chromatic index of a graph" @default.
- W4288242577 doi "https://doi.org/10.48550/arxiv.1909.00150" @default.
- W4288242577 hasPublicationYear "2019" @default.
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