Matching preclusion number of graphs
Zhao Wang, Yaping Mao, Eddie Cheng, Jinyu Zou
TL;DR
This paper studies the matching preclusion number of graphs, providing bounds, characterizations, and exploring extremal and Nordhaus-Gaddum-type relations to deepen understanding of graph resilience against edge removals.
Contribution
It introduces new bounds, characterizations, and extremal problems related to the matching preclusion number, advancing theoretical understanding in graph theory.
Findings
Established sharp upper and lower bounds for the matching preclusion number.
Characterized graphs with extremal matching preclusion numbers.
Explored extremal and Nordhaus-Gaddum-type relations for the matching preclusion number.
Abstract
The \emph{matching preclusion number} of a graph , denoted by , is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. In this paper, we first give some sharp upper and lower bounds of matching preclusion number. Next, graphs with large and small matching preclusion number are characterized, respectively. In the end, we investigate some extremal problems and the Nordhaus-Gaddum-type relations on matching preclusion number.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Interconnection Networks and Systems