论文标题
几乎完整图中的分数三角分解
Fractional triangle decompositions in almost complete graphs
论文作者
论文摘要
我们证明，每个$ n $ vertex图具有至少$ \ binom {n} {2} - （n -4）$ edges具有分数三角分解，以$ n \ ge 7 $。这是我们证明的关键要素，在同伴论文中给出，每$ n $ vertex $ 2 $颜色的完整图包含$ n^2/12 + o（n^2）$ edge-disshewient syhotic triangals，这证实了Erdős的猜想。
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.
