The unbalance of set systems

Nathan Lemons; Cory Palmer

doi:10.1007/s00373-008-0793-9

The unbalance of set systems

Nathan Lemons, Cory Palmer

Mathematical Sciences

Central European University

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

17 Scopus citations

Abstract

The unbalance of an intersecting family F is defined as |F| -d(F), where d(F) is the maximum degree of F i.e. the maximum of |{F ∈ F : x ∈ F}| over all vertices x. We show that the unbalance of a k-uniform intersecting family is at most (_k-2^n-3) when n ≥ 6k³ and we determine all families achieving this bound.

Original language	English
Pages (from-to)	361-365
Number of pages	5
Journal	Graphs and Combinatorics
Volume	24
Issue number	4
DOIs	https://doi.org/10.1007/s00373-008-0793-9
State	Published - Sep 2008

Keywords

Intersecting families
Intersecting set systems

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10.1007/s00373-008-0793-9

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title = "The unbalance of set systems",

abstract = "The unbalance of an intersecting family F is defined as |F| -d(F), where d(F) is the maximum degree of F i.e. the maximum of |\{F ∈ F : x ∈ F\}| over all vertices x. We show that the unbalance of a k-uniform intersecting family is at most (k-2n-3) when n ≥ 6k3 and we determine all families achieving this bound.",

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AU - Palmer, Cory

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N2 - The unbalance of an intersecting family F is defined as |F| -d(F), where d(F) is the maximum degree of F i.e. the maximum of |{F ∈ F : x ∈ F}| over all vertices x. We show that the unbalance of a k-uniform intersecting family is at most (k-2n-3) when n ≥ 6k3 and we determine all families achieving this bound.

AB - The unbalance of an intersecting family F is defined as |F| -d(F), where d(F) is the maximum degree of F i.e. the maximum of |{F ∈ F : x ∈ F}| over all vertices x. We show that the unbalance of a k-uniform intersecting family is at most (k-2n-3) when n ≥ 6k3 and we determine all families achieving this bound.

KW - Intersecting families

KW - Intersecting set systems

UR - https://www.scopus.com/pages/publications/51849118413

U2 - 10.1007/s00373-008-0793-9

DO - 10.1007/s00373-008-0793-9

M3 - Article

AN - SCOPUS:51849118413

SN - 0911-0119

VL - 24

SP - 361

EP - 365

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 4

ER -

The unbalance of set systems

Abstract

Keywords

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