Large Independent Sets in Triangle-Free Planar Graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10312993" target="_blank" >RIV/00216208:11320/14:10312993 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/chapter/10.1007%2F978-3-662-44777-2_29" target="_blank" >http://link.springer.com/chapter/10.1007%2F978-3-662-44777-2_29</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-662-44777-2_29" target="_blank" >10.1007/978-3-662-44777-2_29</a>

Result language
angličtina
Original language name
Large Independent Sets in Triangle-Free Planar Graphs
Original language description
Every triangle-free planar graph on n vertices has an independent set of size at least (n + 1)/3, and this lower bound is tight. We give an algorithm that, given a triangle-free planar graph G on n vertices and an integer k }= 0, decides whether G has anindependent set of size at least (n+k)/3, in time 2(O(root k)) n. Thus, the problem is fixed-parameter tractable when parameterized by k. Furthermore, as a corollary of the result used to prove the correctness of the algorithm, we show that there existsepsilon > 0 such that every planar graph of girth at least five on n vertices has an independent set of size at least n/(3-epsilon).
Czech name
—
Czech description
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Project
<a href="/en/project/LL1201" target="_blank" >LL1201: Complex Structures: Regularities in Combinatorics and Discrete Mathematics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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