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Regular spanning subgraphs of bipartite graphs of high minimum degree
The electronic journal of combinatorics, Tome 14 (2007)

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Let $G$ be a simple balanced bipartite graph on $2n$ vertices, $\delta = \delta(G)/n$, and $\rho_0={\delta + \sqrt{2 \delta -1} \over 2}$. If $\delta \ge 1/2$ then $G$ has a $\lfloor \rho_0 n \rfloor$-regular spanning subgraph. The statement is nearly tight.
DOI : 10.37236/1022
Classification : 05C70, 05C12
Mots-clés : spanning subgraph, factors of graphs, bipartite graph, bipartition, spanning regular subgraph 
Béla Csaba. Regular spanning subgraphs of bipartite graphs of high minimum degree. The electronic journal of combinatorics, Tome 14 (2007). doi: 10.37236/1022
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     author = {B\'ela Csaba},
     title = {Regular spanning subgraphs of bipartite graphs of high minimum degree},
     journal = {The electronic journal of combinatorics},
     year = {2007},
     volume = {14},
     doi = {10.37236/1022},
     zbl = {1157.05322},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1022/}
}
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