Tiling transitive tournaments and their blow-ups

dc.creatorYuster, Raphael
dc.date2002-10-22
dc.date.accessioned2026-07-07T04:52:13Z
dc.date.available2026-07-07T04:52:13Z
dc.descriptionLet $TT_k$ denote the transitive tournament on $k$ vertices. Let $TT(h,k)$ denote the graph obtained from $TT_k$ by replacing each vertex with an independent set of size $h \geq 1$. The following result is proved: Let $c_2=1/2$, $c_3=5/6$ and $c_k=1-2^{-k-\log k}$ for $k \geq 4$. For every $ε> 0$ there exists $N=N(ε,h,k)$ such that for every undirected graph $G$ with $n > N$ vertices and with $δ(G) \geq c_kn$, every orientation of $G$ contains vertex disjoint copies of $TT(h,k)$ that cover all but at most $εn$ vertices. In the cases $k=2$ and $k=3$ the result is asymptotically tight. For $k \geq 4$, $c_k$ cannot be improved to less than $1-2^{-0.5k(1+o(1))}$.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/math/0210338
dc.identifierhttp://arxiv.org/abs/math/0210338
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65388
dc.subjectCombinatorics
dc.subject05C20
dc.titleTiling transitive tournaments and their blow-ups
dc.typetext

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