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On the Bollobás-Eldrige conjecture for bipartite graphs. (English) Zbl 1136.05029
The following result, a special case of the notorious Bollobás-Eldridge conjecture, is proved. If $\Delta_1\geq\Delta_2\geq 2$ are integers, then there exist a natural number $n_0$ and a real $\beta<\Delta_2 /(\Delta_2+1)$ such that if $n\geq n_0$, $H$ and $G$ are graphs on $n$ vertices, $H$ is bipartite with maximal degrees $\Delta_1$, $\Delta_2$ on the respective sides, $G$ has minimal degree $>\beta n$, then $H$ can be placed into $G$. The involved proof uses the Regularity Lemma and a variant (formulated and proved by the author) of the Blow Up Lemma of J. Komlós, G. N. Sárközy, and E. Szemerédi.

05C35Extremal problems (graph theory)
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