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' + 15 in case of non-orientable surface of Euler genus g'. 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
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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
<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
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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