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arXiv · 1612.05381

Erd\H{o}s-Gallai-type results for total monochromatic connection of graphs

Hui Jiang·Xueliang Li·Yingying Zhang
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Abstract

A graph is said to be {\it total-colored} if all the edges and the vertices of the graph are colored. A total-coloring of a graph is a {\it total monochromatically-connecting coloring} ({\it TMC-coloring}, for short) if any two vertices of the graph are connected by a path whose edges and internal vertices have the same color. For a connected graph $G$, the {\it total monochromatic connection number}, denoted by $tmc(G)$, is defined as the maximum number of colors used in a TMC-coloring of $G$. In this paper, we study two kinds of Erd\H{o}s-Gallai-type problems for $tmc(G)$ and completely solve them.

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Hui Jiang, Xueliang Li, Yingying Zhang. 2016-12-16. Erd\H{o}s-Gallai-type results for total monochromatic connection of graphs. https://arxiv.org/abs/1612.05381

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