Cops, a fast robber and defensive domination on interval graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10387176" target="_blank" >RIV/00216208:11320/19:10387176 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=exNqtDCMBw" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=exNqtDCMBw</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.tcs.2018.09.031" target="_blank" >10.1016/j.tcs.2018.09.031</a>

Result language
angličtina
Original language name
Cops, a fast robber and defensive domination on interval graphs
Original language description
The game of Cops and oo-fast Robber is played by two players, one controlling c cops, the other one robber. The players alternate in turns: all the cops move at once to distance at most one each, the robber moves along any cop-free path. Cops win by sharing a vertex with the robber, the robber by avoiding capture indefinitely. The game was proposed with bounded robber speed by Fomin et al. in "Pursuing a fast robber on a graph", generalizing a well-known game of Cops and Robber which has robber speed 1. We answer their open question about the computational complexity of the game on interval graphs with oo-fast robber, showing it to be polynomially decidable. We also generalize the concept of k-defensive domination introduced by Farley and Proskurowski in "Defensive Domination" to A-defensive domination and use it as a main tool in our proof. The generalization allows specifying arbitrary attacks and limiting the number of defenders of each vertex. While this problem is NP-complete even for split graphs, we show that A-defensive domination is decidable in polynomial time on interval graphs.
Czech name
—
Czech description
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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)

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)

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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