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

Csaba, Bela

March 2003, 29 pages.

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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  AUTHOR = {Csaba, Bela},
  TITLE = {On the Bollob\'as -- Eldridge conjecture for bipartite graphs},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2003-1-009},
  MONTH = {March},
  YEAR = {2003},
  ISSN = {0946-011X},