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arXiv · 1812.10701

Erdös-Gallai-type results for conflict-free connection of graphs

Meng Ji·Xueliang Li
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Abstract

A path in an edge-colored graph is called \emph{a conflict-free path} if there exists a color used on only one of its edges. An edge-colored graph is called \emph{conflict-free connected} if there is a conflict-free path between each pair of distinct vertices. The \emph{conflict-free connection number} of a connected graph $G$, denoted by $\mathit{cfc}(G)$, is defined as the smallest number of colors that are required to make $G$ conflict-free connected. In this paper, we obtain Erdös-Gallai-type results for the conflict-free connection numbers of graphs.

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Meng Ji, Xueliang Li. 2018-12-27. Erdös-Gallai-type results for conflict-free connection of graphs. https://arxiv.org/abs/1812.10701

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