Fractional matching preclusion number of graphs
Jinyu Zou, Yaping Mao, Zhao Wang, Eddie Cheng
TL;DR
This paper introduces the fractional matching preclusion number of graphs, providing bounds, characterizations of extremal graphs, and exploring related extremal problems to deepen understanding of fractional perfect matchings.
Contribution
It establishes sharp bounds, characterizes graphs with extreme fractional matching preclusion numbers, and investigates extremal problems, advancing theoretical understanding in graph matchings.
Findings
Sharp bounds for fractional matching preclusion number
Characterizations of graphs with large and small fractional matching preclusion numbers
Analysis of extremal problems related to fractional matching preclusion
Abstract
The \emph{fractional matching preclusion number} of a graph , denoted by , is the minimum number of edges whose deletion results in a graph that has no fractional perfect matchings. In this paper, we first give some sharp upper and lower bounds of fractional matching preclusion number. Next, graphs with large and small fractional matching preclusion number are characterized, respectively. In the end, we investigate some extremal problems on fractional matching preclusion number.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Limits and Structures in Graph Theory