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arXiv · 2008.05313

Fractional triangle decompositions in almost complete graphs

Vytautas Gruslys·Shoham Letzter
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Abstract

We prove that every $n$-vertex graph with at least $\binom{n}{2} - (n - 4)$ edges has a fractional triangle decomposition, for $n \ge 7$. This is a key ingredient in our proof, given in a companion paper, that every $n$-vertex $2$-coloured complete graph contains $n^2/12 + o(n^2)$ edge-disjoint monochromatic triangles, which confirms a conjecture of Erdős.

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Vytautas Gruslys, Shoham Letzter. 2020-08-14. Fractional triangle decompositions in almost complete graphs. https://arxiv.org/abs/2008.05313

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