Decomposing Random Graphs into Few Cycles and Edges

Dániel Korándi; Michael Krivelevich; Benny Sudakov

doi:10.1017/S0963548314000844

Decomposing Random Graphs into Few Cycles and Edges

Dániel Korándi, Michael Krivelevich, Benny Sudakov

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

Over 50 years ago, ErdÅs 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 →. 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.

Original language	English
Pages (from-to)	857-872
Number of pages	16
Journal	Combinatorics Probability and Computing
Volume	24
Issue number	6
DOIs	https://doi.org/10.1017/S0963548314000844
State	Published - 1 Nov 2015

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Statistics and Probability
Computational Theory and Mathematics
Applied Mathematics

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abstract = "Over 50 years ago, Erd{\AA}s 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 →. 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.",

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Decomposing Random Graphs into Few Cycles and Edges

Abstract

All Science Journal Classification (ASJC) codes

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