Erdős-Gallai-Type Results for Total Monochromatic Connection of Graphs

Discussiones Mathematicae Graph Theory

Jiang Hui¹  Zhang Yingying¹  Li Xueliang¹ 

[1] Center for Combinatorics and LPMC, Nankai University, Tianjin300071, China;

关键词: total-colored graph;    total monochromatic connection;    erdős- gallai-type problem;    05c15;    05c35;    05c38;    05c40;   

DOI  :  10.7151/dmgt.2095

来源: DOAJ

【 摘 要 】

A graph is said to be total-colored if all the edges and the vertices of the graph are colored. A total-coloring of a graph is a total monochromatically-connecting coloring (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 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 Erdős-Gallai-type problems for tmc(G) and completely solve them.

【 授权许可】

Unknown