Erdős-Gallai-type results for colorful monochromatic connectivity of a graph
Cai, Qingqiong · Li, Xueliang · Wu, Di
Original · EN
A path in an edge-colored graph is called a monochromatic path if all the edges on the path are colored the same. An edge-coloring of G is a monochromatic connection coloring (MC-coloring, for short) if there is a monochromatic path joining any two vertices in G. The monochromatic connection number, denoted by mc(G), is defined to be the maximum number of colors used in an MC-coloring of a graph G. These concepts were introduced by Caro and Yuster, and they got some nice results. In this paper, we will study two kinds of Erdős-Gallai-type problems for mc(G), and completely solve them.
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