Geodesic
Maximum size of a graph with given fractional matching number
The electronic journal of combinatorics, Tome 29 (2022) no. 3
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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 $r=2$.
DOI : 10.37236/11022
Classification : 05C35, 05C70, 05C72
Mots-clés : fractional matching number, extremal problems 
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     author = {Tianlong Ma and Jianguo Qian and Chao Shi},
     title = {Maximum size of a graph with given fractional matching number},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {3},
     doi = {10.37236/11022},
     zbl = {1510.05148},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/11022/}
}
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Tianlong Ma; Jianguo Qian; Chao Shi. Maximum size of a graph with given fractional matching number. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/11022

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