Maximum Size of a Graph with Given Fractional Matching Number
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Published:2022-09-09
Issue:3
Volume:29
Page:
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ISSN:1077-8926
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Container-title:The Electronic Journal of Combinatorics
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language:
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Short-container-title:Electron. J. Combin.
Author:
Ma Tianlong,Qian Jianguo,Shi Chao
Abstract
For three integers $n,k,d$, we determine the maximum size of a graph on $n$ vertices with fractional matching number $k$ and maximum degree at most $d$. As a consequence, we obtain the maximum size of a graph with given number of vertices and fractional matching number. This partially confirms a conjecture proposed by Alon et al. on the maximum size of $r$-uniform hypergraph with a fractional matching number for the special case when $r=2$.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
1 articles.
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