On the m-eternal Domination Number of Cactus Graphs
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
On the m-eternal Domination Number of Cactus Graphs
Original language description
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.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Reachability Problems
ISBN
978-3-030-30805-6
ISSN
0302-9743
e-ISSN
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Number of pages
15
Pages from-to
33-47
Publisher name
Springer, Cham
Place of publication
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Event location
Brussels
Event date
Sep 11, 2019
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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