MPI-I-2003-1-009
On the Bollob\'as -- Eldridge conjecture for bipartite graphs
Csaba, Bela
March 2003, 29 pages.
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Status: available - back from printing
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
$H \subset G$.
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URL to this document: https://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/2003-1-009
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