Triangle-free planar graphs with small independence number

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10401433" target="_blank" >RIV/00216208:11320/19:10401433 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=vLWtsrBAQg" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=vLWtsrBAQg</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ejc.2018.09.008" target="_blank" >10.1016/j.ejc.2018.09.008</a>

Result language
angličtina
Original language name
Triangle-free planar graphs with small independence number
Original language description
Since planar triangle-free graphs are 3-colourable, such a graph with n vertices has an independent set of size at least nDIVISION SLASH3. We prove that unless the graph contains a certain obstruction, its independence number is at least nDIVISION SLASH(3-ε) for some fixed ε>0. We also provide a reduction rule for this obstruction, which enables us to transform any plane triangle-free graph G into a plane triangle-free graph G' such that α(G')-|G'|DIVISION SLASH3=α(G)-|G|DIVISION SLASH3 and|G'|<=(α(G)-|G|DIVISION SLASH3)DIVISION SLASHε. We derive a number of algorithmic consequences as well as a structural description of n-vertex plane triangle-free graphs whose independence number is close to nDIVISION SLASH3.
Czech name
—
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA14-19503S" target="_blank" >GA14-19503S: Graph coloring and structure</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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