Monochromatic disconnection: Erdős-Gallai-type problems and product graphs

Ping Li () and Xueliang Li ()
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Ping Li: Center for Combinatorics and LPMC, Nankai University
Xueliang Li: Center for Combinatorics and LPMC, Nankai University

Journal of Combinatorial Optimization, 2022, vol. 44, issue 1, No 7, 136-153

Abstract: Abstract For an edge-colored graph G, we call an edge-cut M of G monochromatic if the edges of M are colored with a same color. The graph G is called monochromatically disconnected if any two distinct vertices of G are separated by a monochromatic edge-cut. The monochromatic disconnection number, denoted by md(G), of a connected graph G is the maximum number of colors that are allowed to make G monochromatically disconnected. In this paper, we solve the Erdős-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: Monochromatic edge-cut; Monochromatic disconnection (coloring) number; Erdős-Gallai-type problems; Graph products; 05C15; 05C40; 05C35 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00820-3

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