A Generalization of Erdős' Matching Conjecture
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
A Generalization of Erdős' Matching Conjecture
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GJ16-07822Y" target="_blank" >GJ16-07822Y: Extremal graph theory and applications</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal of Combinatorics
ISSN
1077-8926
e-ISSN
—
Volume of the periodical
25
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
10
Pages from-to
P2.21
UT code for WoS article
000432170100005
EID of the result in the Scopus database
2-s2.0-85046900752