Cops and Robbers on intersection graphs

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Cops and Robbers on intersection graphs

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Cops and Robbers on intersection graphs

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

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

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

European Journal of Combinatorics

ISSN

0195-6698

e-ISSN

—

Svazek periodika

72

Číslo periodika v rámci svazku

August 2018

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

25

Strana od-do

45-69

Kód UT WoS článku

000437075300004

EID výsledku v databázi Scopus

2-s2.0-85046652151