Forbidden induced pairs for perfectness and omega-colourability of graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F22%3A00128976" target="_blank" >RIV/00216224:14330/22:00128976 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.37236/10708" target="_blank" >https://doi.org/10.37236/10708</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.37236/10708" target="_blank" >10.37236/10708</a>
Alternative languages
Result language
angličtina
Original language name
Forbidden induced pairs for perfectness and omega-colourability of graphs
Original language description
We characterise the pairs of graphs {X, Y} such that all {X, Y}-free graphs (distinct from C-5) are perfect. Similarly, we characterise pairs {X, Y} such that all {X, Y}-free graphs (distinct from C-5) are omega-colourable (that is, their chromatic number is equal to their clique number). More generally, we show characterizations of pairs {X, Y} for perfectness and omega-colourability of all connected {X, Y}-free graphs which are of independence at least 3, distinct from an odd cycle, and of order at least n(0), and similar characterisations subject to each subset of these additional constraints. (The classes are non-hereditary and the characterisations for perfectness and omega-colourability are different.) We build on recent results of Brause et al. on {K-1,K-3, Y}-free graphs, and we use Ramsey's Theorem and the Strong Perfect Graph Theorem as main tools. We relate the present characterisations to known results on forbidden pairs for chi-boundedness and deciding k-colourability in polynomial time.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal of Combinatorics
ISSN
1077-8926
e-ISSN
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Volume of the periodical
29
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
33
Pages from-to
1-33
UT code for WoS article
000797338500001
EID of the result in the Scopus database
2-s2.0-85129466862