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- W3181672760 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) ≤ α(G) for any connected graph G, and give an example to show that the bound is sharp. With this result, we prove that if T is a tree with $$Delta(T)geqfrac{alpha(T)+2}{2}$$ , then cfc(T) = Δ(T)." @default.
- W3181672760 created "2021-07-19" @default.
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- W3181672760 date "2021-04-01" @default.
- W3181672760 modified "2023-10-05" @default.
- W3181672760 title "Conflict-free Connection Number and Independence Number of a Graph" @default.
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- W3181672760 doi "https://doi.org/10.1007/s10255-021-1013-0" @default.
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