Forbidden induced pairs for perfectness and ω-colourability of graphs
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F22%3A43965408" target="_blank" >RIV/49777513:23520/22:43965408 - 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 ω-colourability of graphs
Original language description
We characterise the pairs of graphs {X, Y} such that all {X, Y}-free graphs(distinct from C5) are perfect. Similarly, we characterise pairs {X, Y} such that all {X, Y}-free graphs (distinct from C5) are ω-colourable (that is, their chromatic number is equal to their clique number). More generally, we show characterizations of pairs {X, Y} for perfectness and ωcolourability of all connected {X, Y}-free graphs which are of independence at least 3, distinct from an odd cycle, and of order at least n0, and similar characterisations subject to each subset of these additional constraints. (The classes are non-hereditary and the characterisations for perfectness and ω-colourability are different.) We build on recent results of Brause et al. on {K(1,3), 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 χ-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
10101 - Pure mathematics
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
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
1077-8926
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
nestrankovano
UT code for WoS article
000797338500001
EID of the result in the Scopus database
2-s2.0-85129466862