Induced odd cycle packing number, independent sets, and chromatic number

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10473808" target="_blank" >RIV/00216208:11320/23:10473808 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=JiDIp0EpWF" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=JiDIp0EpWF</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/jgt.22932" target="_blank" >10.1002/jgt.22932</a>

Result language
angličtina
Original language name
Induced odd cycle packing number, independent sets, and chromatic number
Original language description
The induced odd cycle packing number iocp(G) of a graph G is the maximum integer k such that G contains an induced subgraph consisting of k pairwise vertex-disjoint odd cycles. Motivated by applications to geometric graphs, Bonamy et al. proved that graphs of bounded induced odd cycle packing number, bounded Vapnik-Chervonenkis (VC) dimension, and linear independence number admit a randomized efficient polynomial-time approximation scheme for the independence number. We show that the assumption of bounded VC dimension is not necessary, exhibiting a randomized algorithm that for any integers k >= 0 and t >= 1 and any n-vertex graph G of induced odd cycle packing number at most k returns in time O-k,O-t(n(k+4)) an independent set of G whose size is at least alpha(G)-n/t (G)-n with high probability. In addition, we present chi-boundedness results for graphs with bounded odd cycle packing number, and use them to design a quasipolynomial-time approximation scheme for the independence number only assuming bounded induced odd cycle packing number.
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
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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
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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