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On the Bollob\'as -- Eldridge conjecture for bipartite graphs

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons44270

Csaba,  Bela
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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2003-1-009
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Csaba, B.(2003). On the Bollob\'as -- Eldridge conjecture for bipartite graphs (MPI-I-2003-1-009). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-6B3A-F
Abstract
Let $G$ be a simple graph on $n$ vertices. A conjecture of Bollob\'as and Eldridge~\cite{be78} asserts that if $\delta (G)\ge {kn-1 \over k+1}$ then $G$ contains any $n$ vertex graph $H$ with $\Delta(H) = k$. We strengthen this conjecture: we prove that if $H$ is bipartite, $3 \le \Delta(H)$ is bounded and $n$ is sufficiently large , then there exists $\beta >0$ such that if $\delta (G)\ge {\Delta \over {\Delta +1}}(1-\beta)n$, then $H \subset G$.