Forbidden induced subgraphs for perfectness of claw-free graphs of independence number at least 4

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F22%3A43965406" target="_blank" >RIV/49777513:23520/22:43965406 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.disc.2022.112837" target="_blank" >https://doi.org/10.1016/j.disc.2022.112837</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2022.112837" target="_blank" >10.1016/j.disc.2022.112837</a>

Result language
angličtina
Original language name
Forbidden induced subgraphs for perfectness of claw-free graphs of independence number at least 4
Original language description
For every graph X, we consider the class of all connected {K(1,3), X}-free graphs which are distinct from an odd cycle and have independence number at least 4, and we show that all graphs in the class are perfect if and only if X is an induced subgraph of some of P6, K1 ∪ P5, 2P3, Z2 or K1 ∪ Z1. Furthermore, for X chosen as 2K1 ∪ K3, we list all eight imperfect graphs belonging to the class; and for every other choice of X, we show that there are infinitely many such graphs. In addition, for X chosen as B(1,2), we describe the structure of all imperfect graphs in the class.
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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA20-09525S" target="_blank" >GA20-09525S: Structural properties of graph classes characterized by forbidden subgraphs</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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