INDEPENDENCE NUMBER IN TRIANGLE-FREE GRAPHS AVOIDING A CLIQUE MINOR

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10511826" target="_blank" >RIV/00216208:11320/25:10511826 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jBu3SxzX7" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=jBu3SxzX7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1090/proc/16069" target="_blank" >10.1090/proc/16069</a>

Jazyk výsledku

angličtina

Název v původním jazyce

INDEPENDENCE NUMBER IN TRIANGLE-FREE GRAPHS AVOIDING A CLIQUE MINOR

Popis výsledku v původním jazyce

The celebrated Hadwiger&apos;s conjecture states that if a graph contains no Kt+1 minor then it is t-colorable. If true, it would in particular imply that every n-vertex Kt+1-minor-free graph has an independent set of size at least n/t. In 1982, Duchet and Meyniel proved that this bound holds within a factor 2. Their bound has been improved; most notably by a constant factor by Fox, which was later improved by Balogh and Kostochka. Here we consider the same question for triangle-free graphs. By the results of Shearer and Kostochka and Thomason, it follows that any triangle-free n-vertex graph with no Omega(root log t/t n) minor has an independent set of size Omega( t n). We show that a much larger independent set exists; for every positive epsilon &lt; 1/26 and sufficiently large t, every triangle-free graph on n vertices with no Kt-minor has an independent set of size n/t(1)-epsilon . This answers a question of Sergey Norin.

Název v anglickém jazyce

INDEPENDENCE NUMBER IN TRIANGLE-FREE GRAPHS AVOIDING A CLIQUE MINOR

Popis výsledku anglicky

The celebrated Hadwiger&apos;s conjecture states that if a graph contains no Kt+1 minor then it is t-colorable. If true, it would in particular imply that every n-vertex Kt+1-minor-free graph has an independent set of size at least n/t. In 1982, Duchet and Meyniel proved that this bound holds within a factor 2. Their bound has been improved; most notably by a constant factor by Fox, which was later improved by Balogh and Kostochka. Here we consider the same question for triangle-free graphs. By the results of Shearer and Kostochka and Thomason, it follows that any triangle-free n-vertex graph with no Omega(root log t/t n) minor has an independent set of size Omega( t n). We show that a much larger independent set exists; for every positive epsilon &lt; 1/26 and sufficiently large t, every triangle-free graph on n vertices with no Kt-minor has an independent set of size n/t(1)-epsilon . This answers a question of Sergey Norin.

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/GA17-04611S" target="_blank" >GA17-04611S: Ramseyovské aspekty barvení grafů</a><br>

Návaznosti

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

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Proceedings of the American Mathematical Society

ISSN

0002-9939

e-ISSN

1088-6826

Svazek periodika

153

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

11

Strana od-do

3185-3195

Kód UT WoS článku

001520003400001

EID výsledku v databázi Scopus

2-s2.0-105009253037