On the m-eternal Domination Number of Cactus Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F19%3A00333858" target="_blank" >RIV/68407700:21240/19:00333858 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/chapter/10.1007/978-3-030-30806-3_4" target="_blank" >https://link.springer.com/chapter/10.1007/978-3-030-30806-3_4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-30806-3_4" target="_blank" >10.1007/978-3-030-30806-3_4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the m-eternal Domination Number of Cactus Graphs

Popis výsledku v původním jazyce

Given a graph $G$, guards are placed on vertices of $G$. Then vertices are subject to an infinite sequence of attacks so that each attack must be defended by a guard moving from a neighboring vertex. The m-eternal domination number is the minimum number of guards such that the graph can be defended indefinitely. In this paper we study the m-eternal domination number of cactus graphs, that is, connected graphs where each edge lies in at most two cycles, and we consider three variants of the m-eternal domination number: first variant allows multiple guards to occupy a single vertex, second variant does not allow it, and in the third variant additional ``eviction'' attacks must be defended. We provide a new upper bound for the m-eternal domination number of cactus graphs, and for a subclass of cactus graphs called Christmas cactus graphs, where each vertex lies in at most two cycles, we prove that these three numbers are equal. Moreover, we present a linear-time algorithm for computing them.

Název v anglickém jazyce

On the m-eternal Domination Number of Cactus Graphs

Popis výsledku anglicky

Given a graph $G$, guards are placed on vertices of $G$. Then vertices are subject to an infinite sequence of attacks so that each attack must be defended by a guard moving from a neighboring vertex. The m-eternal domination number is the minimum number of guards such that the graph can be defended indefinitely. In this paper we study the m-eternal domination number of cactus graphs, that is, connected graphs where each edge lies in at most two cycles, and we consider three variants of the m-eternal domination number: first variant allows multiple guards to occupy a single vertex, second variant does not allow it, and in the third variant additional ``eviction'' attacks must be defended. We provide a new upper bound for the m-eternal domination number of cactus graphs, and for a subclass of cactus graphs called Christmas cactus graphs, where each vertex lies in at most two cycles, we prove that these three numbers are equal. Moreover, we present a linear-time algorithm for computing them.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

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

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název statě ve sborníku

Reachability Problems

ISBN

978-3-030-30805-6

ISSN

0302-9743

e-ISSN

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Počet stran výsledku

15

Strana od-do

33-47

Název nakladatele

Springer, Cham

Místo vydání

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Místo konání akce

Brussels

Datum konání akce

11. 9. 2019

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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