An Erdos-Ko-Rado theorem for unions of length 2 paths
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10420394" target="_blank" >RIV/00216208:11320/20:10420394 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_ah.lgPJhr" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=_ah.lgPJhr</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2020.112121" target="_blank" >10.1016/j.disc.2020.112121</a>
Alternative languages
Result language
angličtina
Original language name
An Erdos-Ko-Rado theorem for unions of length 2 paths
Original language description
A family of sets is intersecting if any two sets in the family intersect. Given a graph G and an integer r >= 1, let I-(r)(G) denote the family of independent sets of size r of G. For a vertex v of G, the family of independent sets of size r that contain v is called an r-star. Then G is said to be r-EKR if no intersecting subfamily of I-(r)(G) is bigger than the largest r-star. Let n be a positive integer, and let G consist of the disjoint union of n paths each of length 2. We prove that if 1 <= r <= n/2, then G is r-EKR. This affirms a longstanding conjecture of Holroyd and Talbot for this class of graphs and can be seen as an analogue of a well-known theorem on signed sets, proved using different methods, by Deza and Frankl and by Bollobas and Leader. Our main approach is a novel probabilistic extension of Katona's elegant cycle method, which might be of independent interest. (c) 2020 Elsevier B.V. All rights reserved.
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
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA19-21082S" target="_blank" >GA19-21082S: Graphs and their algebraic properties</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete Mathematics
ISSN
0012-365X
e-ISSN
—
Volume of the periodical
343
Issue of the periodical within the volume
12
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
6
Pages from-to
112121
UT code for WoS article
000579057200033
EID of the result in the Scopus database
2-s2.0-85089850535