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Cops and Robbers on intersection graphs

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384801" target="_blank" >RIV/00216208:11320/18:10384801 - isvavai.cz</a>

  • Result on the web

    <a href="https://doi.org/10.1016/j.ejc.2018.04.009" target="_blank" >https://doi.org/10.1016/j.ejc.2018.04.009</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.ejc.2018.04.009" target="_blank" >10.1016/j.ejc.2018.04.009</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Cops and Robbers on intersection graphs

  • Original language description

    The cop number of a graph G is the smallest k such that k cops win the game of cops and robber on G. We investigate the maximum cop number of geometric intersection graphs, which are graphs whose vertices are represented by geometric shapes and edges by their intersections. We establish the following dichotomy for previously studied classes of intersection graphs: The intersection graphs of arc-connected sets in the plane (called string graphs) have cop number at most 15, and more generally, the intersection graphs of arc-connected subsets of a surface have cop number at most 10g + 15 in case of orientable surface of genus g, and at most 10g&apos; + 15 in case of non-orientable surface of Euler genus g&apos;. For more restricted classes of intersection graphs, we obtain better bounds: the maximum cop number of interval filament graphs is two, and the maximum cop number of outer-string graphs is between 3 and 4. The intersection graphs of disconnected 2-dimensional sets or of 3-dimensional sets have unbounded cop number even in very restricted settings. For instance, it follows from known results that the cop number is unbounded on intersection graphs of two-element subsets of a line. We further show that it is also unbounded on intersection graphs of 3-dimensional unit balls, of 3-dimensional unit cubes or of 3-dimensional axis-aligned unit segments.

  • 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

    <a href="/en/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Center of excellence - Institute for theoretical computer science (CE-ITI)</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2018

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    European Journal of Combinatorics

  • ISSN

    0195-6698

  • e-ISSN

  • Volume of the periodical

    72

  • Issue of the periodical within the volume

    August 2018

  • Country of publishing house

    GB - UNITED KINGDOM

  • Number of pages

    25

  • Pages from-to

    45-69

  • UT code for WoS article

    000437075300004

  • EID of the result in the Scopus database

    2-s2.0-85046652151