Towards the Erdos-Gallai Cycle Decomposition Conjecture

被引：1

作者：

Bucic, Matija ^{[1
,2
]}

Montgomery, Richard ^{[3
]}

机构：

[1] Inst Adv Study, Princeton, NJ 08540 USA

[2] Princeton Univ, Princeton, NJ 08540 USA

[3] Univ Warwick, Coventry, England

来源：

PROCEEDINGS OF THE 55TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING, STOC 2023 | 2023年

基金：

欧洲研究理事会;

关键词：

Robust sublinear expanders; Decomposition into expanders; Graph decomposition; Erdos-Gallai Conjecture; LONG CYCLES; GRAPH; COVERINGS; MINORS; PROOF;

D O I：

10.1145/3564246.3585218

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In the 1960's, Erdos 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(star) n) cycles and edges, where log(star) n is the iterated logarithm function. Our arguments make use and further develop the theory of robust sub-linear expander graphs.

引用

页码：839 / 852

页数：14

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