论文标题
朝向erdős-gallai循环分解猜想
Towards the Erdős-Gallai Cycle Decomposition Conjecture
论文作者
论文摘要
在1960年代，埃尔德（Erd）和加莱（Gallai）猜想，任何$ n $ vertex图的边缘都可以分解为$ o（n）$循环和边缘。 We improve upon the previous best bound of $O(n\log\log n)$ cycles and edges due to Conlon, Fox and Sudakov, by showing an $n$-vertex graph can always be decomposed into $O(n\log^{*}n)$ cycles and edges, where $\log^{*}n$ is the iterated logarithm function.
In the 1960's, Erdős and Gallai conjectured that the edges of any $n$-vertex graph can be decomposed into $O(n)$ cycles and edges. We improve upon the previous best bound of $O(n\log\log n)$ cycles and edges due to Conlon, Fox and Sudakov, by showing an $n$-vertex graph can always be decomposed into $O(n\log^{*}n)$ cycles and edges, where $\log^{*}n$ is the iterated logarithm function.
