H. Jiang, X. Li, Y. Zhang
Erd§s-Gallai-type results for total monochromatic connection of graphs
Discussiones Mathematicae Graph Theory
Received 29.03.2017, Revised 14.11.2017, Accepted 20.11.2017, doi: 10.7151/dmgt.2095
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 Erdös-Gallai-type problems for tmc(G) and completely solve them.
total-colored graph, total monochromatic connection, Erdös-Gallai-type problem