Measures on monotone properties of graphs

Jòzsef Balogh; Béla Bollobás; David Weinreich

doi:10.1016/S0166-218X(01)00175-5

Measures on monotone properties of graphs

Jòzsef Balogh, Béla Bollobás, David Weinreich

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

Abstract

Given a monotone property P of graphs, write P ⁿ for the set of graphs with vertex set [n] having property P. Building on recent results in the enumeration of graphical properties, we prove numerous results about the structure of graphs in P ⁿ and the functions |P ⁿ|. We also examine the measure eP(n), the maximum number of edges in a graph of P ⁿ.

Original language	English (US)
Pages (from-to)	17-36
Number of pages	20
Journal	Discrete Applied Mathematics
Volume	116
Issue number	1-2
DOIs	https://doi.org/10.1016/S0166-218X(01)00175-5
State	Published - Jan 15 2002
Externally published	Yes

Keywords

Extremal graph theory
Graph properties
Hereditary
Monotone
Size
Speed

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Online availability

10.1016/S0166-218X(01)00175-5

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author = "J{\`o}zsef Balogh and B{\'e}la Bollob{\'a}s and David Weinreich",

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AU - Balogh, Jòzsef

AU - Bollobás, Béla

AU - Weinreich, David

N1 - Funding Information: Research partially supported by OTKA grant F026049 and NSF Grant DMS 9971788.

PY - 2002/1/15

Y1 - 2002/1/15

N2 - Given a monotone property P of graphs, write P n for the set of graphs with vertex set [n] having property P. Building on recent results in the enumeration of graphical properties, we prove numerous results about the structure of graphs in P n and the functions |P n|. We also examine the measure eP(n), the maximum number of edges in a graph of P n.

AB - Given a monotone property P of graphs, write P n for the set of graphs with vertex set [n] having property P. Building on recent results in the enumeration of graphical properties, we prove numerous results about the structure of graphs in P n and the functions |P n|. We also examine the measure eP(n), the maximum number of edges in a graph of P n.

KW - Extremal graph theory

KW - Graph properties

KW - Hereditary

KW - Monotone

KW - Size

KW - Speed

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JF - Discrete Applied Mathematics

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ER -

Measures on monotone properties of graphs

Abstract

Keywords

ASJC Scopus subject areas

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