INDEPENDENCE NUMBER IN TRIANGLE-FREE GRAPHS AVOIDING A CLIQUE MINOR

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
INDEPENDENCE NUMBER IN TRIANGLE-FREE GRAPHS AVOIDING A CLIQUE MINOR
Original language description
The celebrated Hadwiger'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 < 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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project
<a href="/en/project/GA17-04611S" target="_blank" >GA17-04611S: Ramsey-like aspects of graph coloring</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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