An Erdos-Ko-Rado theorem for unions of length 2 paths

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

An Erdos-Ko-Rado theorem for unions of length 2 paths

Popis výsledku v původním jazyce

A family of sets is intersecting if any two sets in the family intersect. Given a graph G and an integer r &gt;= 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 &lt;= r &lt;= 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&apos;s elegant cycle method, which might be of independent interest. (c) 2020 Elsevier B.V. All rights reserved.

Název v anglickém jazyce

An Erdos-Ko-Rado theorem for unions of length 2 paths

Popis výsledku anglicky

A family of sets is intersecting if any two sets in the family intersect. Given a graph G and an integer r &gt;= 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 &lt;= r &lt;= 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&apos;s elegant cycle method, which might be of independent interest. (c) 2020 Elsevier B.V. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA19-21082S" target="_blank" >GA19-21082S: Grafy a jejich algebraické vlastnosti</a><br>

Návaznosti

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

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Discrete Mathematics

ISSN

0012-365X

e-ISSN

—

Svazek periodika

343

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

6

Strana od-do

112121

Kód UT WoS článku

000579057200033

EID výsledku v databázi Scopus

2-s2.0-85089850535