A Generalization of Erdős' Matching Conjecture

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F18%3A00489948" target="_blank" >RIV/67985807:_____/18:00489948 - isvavai.cz</a>

Výsledek na webu

<a href="http://hdl.handle.net/11104/0284241" target="_blank" >http://hdl.handle.net/11104/0284241</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.37236/7420" target="_blank" >10.37236/7420</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Generalization of Erdős' Matching Conjecture

Popis výsledku v původním jazyce

Let H = (V,epsilon ) be an r-uniform hypergraph on n vertices and fix a positive integer k such that 1 <= k <= r. A k-matching of H is a collection of edges M subset of epsilon such that every subset of V whose cardinality equals k is contained in at most one element of M. The k-matching number of H is the maximum cardinality of a k-matching. A well-known problem, posed by Erdos, asks for the maximum number of edges in an r-uniform hypergraph under constraints on its 1-matching number. In this article we investigate the more general problem of determining the maximum number of edges in an r-uniform hypergraph on n vertices subject to the constraint that its k-matching number is strictly less than a. The problem can also be seen as a generalization of the well-known k-intersection problem. We propose candidate hypergraphs for the solution of this problem, and show that the extremal hypergraph r is among this candidate set when n >= 4r ((r)(k) )(2). a.

Název v anglickém jazyce

A Generalization of Erdős' Matching Conjecture

Popis výsledku anglicky

Let H = (V,epsilon ) be an r-uniform hypergraph on n vertices and fix a positive integer k such that 1 <= k <= r. A k-matching of H is a collection of edges M subset of epsilon such that every subset of V whose cardinality equals k is contained in at most one element of M. The k-matching number of H is the maximum cardinality of a k-matching. A well-known problem, posed by Erdos, asks for the maximum number of edges in an r-uniform hypergraph under constraints on its 1-matching number. In this article we investigate the more general problem of determining the maximum number of edges in an r-uniform hypergraph on n vertices subject to the constraint that its k-matching number is strictly less than a. The problem can also be seen as a generalization of the well-known k-intersection problem. We propose candidate hypergraphs for the solution of this problem, and show that the extremal hypergraph r is among this candidate set when n >= 4r ((r)(k) )(2). a.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ16-07822Y" target="_blank" >GJ16-07822Y: Extremální teorie grafů a aplikace</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Electronic Journal of Combinatorics

ISSN

1077-8926

e-ISSN

—

Svazek periodika

25

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

P2.21

Kód UT WoS článku

000432170100005

EID výsledku v databázi Scopus

2-s2.0-85046900752