Erdős–Gallai-type results for colorful monochromatic connectivity of a graph

Qingqiong Cai (), Xueliang Li () and Di Wu ()
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Qingqiong Cai: Nankai University
Xueliang Li: Nankai University
Di Wu: Nankai University

Journal of Combinatorial Optimization, 2017, vol. 33, issue 1, No 8, 123-131

Abstract: Abstract A path in an edge-colored graph is called a monochromatic path if all the edges on the path are colored with one same color. 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. For a connected graph G, the monochromatic connection number of G, denoted by mc(G), is defined to be the maximum number of colors used in an MC-coloring of G. These concepts were introduced by Caro and Yuster, and they got some nice results. In this paper, we study two kinds of Erdős–Gallai-type problems for mc(G), and completely solve them.

Keywords: Monochromatic path; MC-coloring; Monochromatic connection number; Erdős–Gallai-type problem; 05C15; 05C35; 05C38; 05C40 (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10878-015-9938-y

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