Monochromatic disconnection: Erd\H{o}s-Gallai-type problems and product graphs
Abstract
For an edge-colored graph , we call an edge-cut of monochromatic if the edges of are colored with a same color. The graph is called monochromatically disconnected if any two distinct vertices of are separated by a monochromatic edge-cut. The monochromatic disconnection number, denoted by , of a connected graph is the maximum number of colors that are allowed to make monochromatically disconnected. In this paper, we solve the Erd\H{o}s-Gallai-type problems for the monochromatic disconnection, and give the monochromatic disconnection numbers for four graph products, i.e., Cartesian, strong, lexicographic, and tensor products.
Keywords
Cite
@article{arxiv.1904.08583,
title = {Monochromatic disconnection: Erd\H{o}s-Gallai-type problems and product graphs},
author = {Ping Li and Xueliang Li},
journal= {arXiv preprint arXiv:1904.08583},
year = {2020}
}
Comments
21 pages, 4 figures. In this new version we obtain the explicit expression for the extremal function $g(n,r)$, which was only an upper bound for the case $3\leq r \leq \lfloor \frac n 2 \rfloor - 1$ in the old version