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- W3089776415 abstract "Given an undirected graph G=(V,E), a conflict-free coloring with respect to open neighborhoods (CFON coloring) is a vertex coloring such that every vertex has a uniquely colored vertex in its open neighborhood. The minimum number of colors required for such a coloring is the CFON chromatic number of G, denoted by χON(G). In previous work [WG 2020], we showed the upper bound χON(G)≤dc(G)+3, where dc(G) denotes the distance to cluster parameter of G. In this paper, we obtain the improved upper bound of χON(G)≤dc(G)+1. We also exhibit a family of graphs for which χON(G)>dc(G), thereby demonstrating that our upper bound is tight." @default.
- W3089776415 created "2020-10-08" @default.
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- W3089776415 date "2022-11-01" @default.
- W3089776415 modified "2023-10-16" @default.
- W3089776415 title "A tight bound for conflict-free coloring in terms of distance to cluster" @default.
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- W3089776415 doi "https://doi.org/10.1016/j.disc.2022.113058" @default.
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