Proof of a conjecture of Bollobas and Eldridge for graphs of maximum degree 
three

Csaba, Bela

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Proof of a conjecture of Bollobas and Eldridge for graphs of maximum degree three

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

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Citation

Csaba, B. (2003). Proof of a conjecture of Bollobas and Eldridge for graphs of maximum degree three. Combinatorica, 23, 35-72.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-2DD3-C

Abstract

Let $G_1$ and $G_2$ be simple graphs on $n$ vertices. If there are edge-disjoint copies of $G_1$ and $G_2$ in $K_n$, then we say there is a packing of $G_1$ and $G_2$. A conjecture of Bollob\'as and Eldridge ~\cite{be78} asserts that if $(\Delta(G_1)+1)(\Delta(G_2)+1)\le n+1$ then there is a packing of $G_1$ and $G_2$. We prove this conjecture when $\Delta(G_1)=3$, for sufficiently large $n$.