Geodesic
Asymptotically optimal tree-packings in regular graphs
The electronic journal of combinatorics, Tome 8 (2001) no. 1
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Let $T$ be a tree with $t$ vertices. Clearly, an $n$ vertex graph contains at most $n/t$ vertex disjoint trees isomorphic to $T$. In this paper we show that for every $\epsilon >0$, there exists a $D(\epsilon,t)>0$ such that, if $d>D(\epsilon,t)$ and $G$ is a simple $d$-regular graph on $n$ vertices, then $G$ contains at least $(1-\epsilon)n/t$ vertex disjoint trees isomorphic to $T$.
DOI : 10.37236/1582
Classification : 05B40, 05C05, 05C35, 05C70, 05D15
Mots-clés : tree-packings, matchings in hypergraphs 
@article{10_37236_1582,
     author = {Alexander Kelmans and Dhruv Mubayi and Benny Sudakov},
     title = {Asymptotically optimal tree-packings in regular graphs},
     journal = {The electronic journal of combinatorics},
     year = {2001},
     volume = {8},
     number = {1},
     doi = {10.37236/1582},
     zbl = {0993.05045},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1582/}
}
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Alexander Kelmans; Dhruv Mubayi; Benny Sudakov. Asymptotically optimal tree-packings in regular graphs. The electronic journal of combinatorics, Tome 8 (2001) no. 1. doi: 10.37236/1582

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