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- W3111492015 abstract "An edge-colored graph $G$ is conflict-free connected if any two of its vertices are connected by a path, which contains a color used on exactly one of its edges. The conflict-free connection number of a connected graph $G$, denoted by $cfc(G)$, is defined as the minimum number of colors that are required in order to make $G$ conflict-free connected. In this paper, we investigate the relation between the conflict-free connection number and the independence number of a graph. We firstly show that $cfc(G)le alpha(G)$ for any connected graph $G$, and an example is given showing that the bound is sharp. With this result, we prove that if $T$ is a tree with $Delta(T)ge frac{alpha(T)+2}{2}$, then $cfc(T)=Delta(T)$." @default.
- W3111492015 created "2020-12-21" @default.
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- W3111492015 date "2020-12-08" @default.
- W3111492015 modified "2023-09-25" @default.
- W3111492015 title "Conflict-free connection number and independence number of a graph" @default.
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- W3111492015 doi "https://doi.org/10.48550/arxiv.2012.04820" @default.
- W3111492015 hasPublicationYear "2020" @default.
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