论文标题
$ O（M）$ - 边缘连接的ed exgumpositions to固定树的同构副本尺寸$ M $
Edge-decompositions of $O(m)$-edge-connected graphs into isomorphic copies of a fixed tree of size $m$
论文作者
论文摘要
在本文中，我们表明，每$ o（m）$ - 边缘连接的简单图$ g $尺寸可除以$ m $，至少$ 2^{o（m）} $具有边缘分解为任何给定的树$ t $ t $ size $ m $的同构副本。此外，对于图形$ g $，可以将最低度条件删除，腰围大于$ t $的直径。由于Bensmail，Harutyunyan，Le，Merker和Thomassé（2017）和Merker（2017），这些结果提高了两个结果，他们对必要的边缘连接性产生了阶乘上限。
In this paper, we show that every $O(m)$-edge-connected simple graph $G$ of size divisible by $m$ with minimum degree at least $2^{O(m)}$ has an edge-decomposition into isomorphic copies of any given tree $T$ of size $m$. Moreover, the minimum degree condition can be dropped for graphs $G$ with girth greater than the diameter of $T$. These results improve two results due to Bensmail, Harutyunyan, Le, Merker, and Thomassé (2017) and Merker (2017) who gave a factorial upper bound on the necessary edge-connectivity.
