Common edge independence number of a tree (Brief Announcement)
Year: 2023
Type: conference-paper
Abstract: The cardinality of a largest matching of G, denoted by α'(G), is called the upper matching number of G. The lower matching number i'(G) of a graph G is the cardinality of a smallest maximal matching of G. We introduce the concept of the common edge independence number of a graph G, denoted by α'c(G), is the largest integer k such that every edge of G belongs to a matching that has at least k edges. For any graph G, the relations between above parameters are given by the chain of inequalities i'(G) ≤ α'c(G) ≤ α'(G). We study relations between this three parameters, in particular we show that the difference between α'c(G) and i'(G) can be arbitrarily large while α'(G) and α'c(G) may differ by at most one. We also characterize the trees T for which i'(T) = α'c(T), and the trees T for which α'c(T) = α'(T).
Source: Procedia Computer Science
Authors: Magda Dettlaff, Magdalena Lemańska, Jerzy Topp
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4386857752