Decomposing Random Graphs into Few Cycles and Edges

被引：4
|
作者：
Korandi, Daniel [1 ]
Krivelevich, Michael [2 ]
Sudakov, Benny [1 ]
机构：
[1] ETH, Dept Math, CH-8092 Zurich, Switzerland
[2] Tel Aviv Univ, Sch Math Sci, Sackler Fac Exact Sci, IL-6997801 Tel Aviv, Israel
来源：
COMBINATORICS PROBABILITY & COMPUTING | 2015年 / 24卷 / 06期
基金：
瑞士国家科学基金会; 以色列科学基金会;
关键词：
D O I：
10.1017/S0963548314000844
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Over 50 years ago, Erdos and Gallai conjectured that the edges of every graph on n vertices can be decomposed into O(n) cycles and edges. Among other results, Conlon, Fox and Sudakov recently proved that this holds for the random graph G(n, p) with probability approaching 1 as n -> infinity. In this paper we show that for most edge probabilities G(n, p) can be decomposed into a union of n/4 + np/2 + o(n) cycles and edges w.h.p. This result is asymptotically tight.
引用
收藏
页码：857 / 872
页数：16
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