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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Result continuities

  • Project

  • 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

  • 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