Fractional triangle decompositions in almost complete graphs

Abstract

We prove that every $n$-vertex graph with at least $\left(\genfrac{}{}{0ex}{}{n}{2}\right)-(n-4)$ 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.

21 pages

References in corpus (1)

• Monochromatic triangle packings in red-blue graphs

Cited by in corpus (1)

• Monochromatic triangle packings in red-blue graphs