Completing Partial Packings of Bipartite Graphs

Details Completing Partial Packings of Bipartite Graphs Completing Partial Packings of Bipartite Graphs

2010-07-24

arxiv.org/abs/1007.4287v3

Mathematics

Combinatorics

Scientific paper

Given a bipartite graph $H$ and an integer $n$, let $f(n;H)$ be the smallest integer such that, any set of edge disjoint copies of $H$ on $n$ vertices, can be extended to an $H$-design on at most $n+f(n;H)$ vertices. We establish tight bounds for the growth of $f(n;H)$ as $n \rightarrow \infty$. In particular, we prove the conjecture of F\"uredi and Lehel \cite{FuLe} that $f(n;H) = o(n)$. This settles a long-standing open problem.

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