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- W2952877655 abstract "A perfect $K_t$-matching in a graph $G$ is a spanning subgraph consisting of vertex disjoint copies of $K_t$. A classic theorem of Hajnal and Szemeredi states that if $G$ is a graph of order $n$ with minimum degree $delta(G) ge (t-1)n/t$ and $t| n$, then $G$ contains a perfect $K_t$-matching. Let $G$ be a $t$-partite graph with vertex classes $V_1$,..., $V_t$ each of size $n$. We show that if every vertex $x in V_i$ is joined to at least $((t-1)/t + gamma)n $ vertices of $V_j$ for $i ne j$, then $G$ contains a perfect $K_t$-matching, thus verifying a conjecture of Fisher asymptotically. Furthermore, we consider a generalisation to hypergraphs in terms of the codegree." @default.
- W2952877655 created "2019-06-27" @default.
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- W2952877655 date "2011-08-21" @default.
- W2952877655 modified "2023-09-24" @default.
- W2952877655 title "A multipartite version of the Hajnal-Szemer'edi theorem for graphs and hypergraphs" @default.
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