Bipartite subgraphs

Noga Alon

doi:10.1007/BF01261315

Bipartite subgraphs

Noga Alon

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

82 Scopus citations

Abstract

It is shown that there exists a positive c so that for any large integer m, any graph with 2m² edges contains a bipartite subgraph with at least m²+m/2+c√m edges. This is tight up to the constant c and settles a problem of Erdos. It is also proved that any triangle-free graph with e>1 edges contains a bipartite subgraph with at least e/2+c′e^4/5 edges for some absolute positive constant c′. This is tight up to the constant c′.

Original language	English
Pages (from-to)	301-311
Number of pages	11
Journal	Combinatorica
Volume	16
Issue number	3
DOIs	https://doi.org/10.1007/BF01261315
State	Published - 1 Jan 1996
Externally published	Yes

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Computational Mathematics

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10.1007/BF01261315

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title = "Bipartite subgraphs",

abstract = "It is shown that there exists a positive c so that for any large integer m, any graph with 2m2 edges contains a bipartite subgraph with at least m2+m/2+c√m edges. This is tight up to the constant c and settles a problem of Erdos. It is also proved that any triangle-free graph with e>1 edges contains a bipartite subgraph with at least e/2+c′e4/5 edges for some absolute positive constant c′. This is tight up to the constant c′.",

author = "Noga Alon",

year = "1996",

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doi = "10.1007/BF01261315",

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AU - Alon, Noga

PY - 1996/1/1

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N2 - It is shown that there exists a positive c so that for any large integer m, any graph with 2m2 edges contains a bipartite subgraph with at least m2+m/2+c√m edges. This is tight up to the constant c and settles a problem of Erdos. It is also proved that any triangle-free graph with e>1 edges contains a bipartite subgraph with at least e/2+c′e4/5 edges for some absolute positive constant c′. This is tight up to the constant c′.

AB - It is shown that there exists a positive c so that for any large integer m, any graph with 2m2 edges contains a bipartite subgraph with at least m2+m/2+c√m edges. This is tight up to the constant c and settles a problem of Erdos. It is also proved that any triangle-free graph with e>1 edges contains a bipartite subgraph with at least e/2+c′e4/5 edges for some absolute positive constant c′. This is tight up to the constant c′.

UR - https://www.scopus.com/pages/publications/0041494491

U2 - 10.1007/BF01261315

DO - 10.1007/BF01261315

M3 - Article

AN - SCOPUS:0041494491

SN - 0209-9683

VL - 16

SP - 301

EP - 311

JO - Combinatorica

JF - Combinatorica

IS - 3

ER -

Bipartite subgraphs

Abstract

ASJC Scopus subject areas

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