LARGE INDEPENDENT SETS IN TRIANGLE-FREE PLANAR GRAPHS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F17%3A10364953" target="_blank" >RIV/00216208:11320/17:10364953 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/16M1061862" target="_blank" >http://dx.doi.org/10.1137/16M1061862</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/16M1061862" target="_blank" >10.1137/16M1061862</a>
Alternative languages
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 an independent 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 exists epsilon > 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). We further give an algorithm that, given a planar graph G of maximum degree 4 on n vertices and an integer k >= 0, decides whether G has an independent set of size at least (n + k)/4, in time 2(O(root k)) n.
Czech name
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Czech description
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Classification
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)
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Discrete Mathematics
ISSN
0895-4801
e-ISSN
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Volume of the periodical
31
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
19
Pages from-to
1355-1373
UT code for WoS article
000404770300036
EID of the result in the Scopus database
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