2016/12/16 by Hui Jiang, Xueliang Li, Jiang, Hui +3
Computer Science · Physics and Astronomy · #05C15 #05C35 #05C38 #05C40 #Advanced Graph Theory Research #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Graph Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.1612.05381
openalex publication_date 2016/12/16 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
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 Erdős-Gallai-type problems for tmc(G) and completely solve them.