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arXiv · 1703.05149

The Bollob\'as-Eldridge-Catlin conjecture for even girth at least $10$

Wouter Cames van Batenburg·Ross J. Kang
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Abstract

Two graphs $G_1$ and $G_2$ on $n$ vertices are said to \textit{pack} if there exist injective mappings of their vertex sets into $[n]$ such that the images of their edge sets are disjoint. A longstanding conjecture due to Bollob\'as and Eldridge and, independently, Catlin, asserts that, if $(\Delta(G_1)+1) (\Delta(G_2)+1) \le n+1$, then $G_1$ and $G_2$ pack. We consider the validity of this assertion under the additional assumptions that neither $G_1$ nor $G_2$ contain a $4$-, $6$- or $8$-cycle, and that $\Delta(G_1)$ or $\Delta(G_2)$ is large enough ($\ge 940060$).

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Wouter Cames van Batenburg, Ross J. Kang. 2017-03-15. The Bollob\'as-Eldridge-Catlin conjecture for even girth at least $10$. https://arxiv.org/abs/1703.05149

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