Complexity of 2-Rainbow Total Domination Problem
In this paper, we extend the findings of recent studies on k -rainbow total domination by placing our focus on its computational complexity aspects. We show that the problem of determining whether a graph has a 2-rainbow total dominating function of a given weight is NP-complete. This complexity res...
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2024-09, Vol.47 (5), Article 155 |
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| creator | Šumenjak, Tadeja Kraner Tepeh, Aleksandra |
| description | In this paper, we extend the findings of recent studies on
k
-rainbow total domination by placing our focus on its computational complexity aspects. We show that the problem of determining whether a graph has a 2-rainbow total dominating function of a given weight is NP-complete. This complexity result holds even when restricted to planar graphs. Along the way tight bounds for the
k
-rainbow total domination number of rooted product graphs are established. In addition, we obtain the closed formula for the
k
-rainbow total domination number of the corona product
G
∗
H
, provided that
H
has enough vertices. |
| doi_str_mv | 10.1007/s40840-024-01747-8 |
| format | Article |
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k
-rainbow total domination by placing our focus on its computational complexity aspects. We show that the problem of determining whether a graph has a 2-rainbow total dominating function of a given weight is NP-complete. This complexity result holds even when restricted to planar graphs. Along the way tight bounds for the
k
-rainbow total domination number of rooted product graphs are established. In addition, we obtain the closed formula for the
k
-rainbow total domination number of the corona product
G
∗
H
, provided that
H
has enough vertices.</description><identifier>ISSN: 0126-6705</identifier><identifier>EISSN: 2180-4206</identifier><identifier>DOI: 10.1007/s40840-024-01747-8</identifier><language>eng</language><publisher>Singapore: Springer Nature Singapore</publisher><subject>Apexes ; Applications of Mathematics ; Complexity ; Graph theory ; Graphs ; Mathematics ; Mathematics and Statistics</subject><ispartof>Bulletin of the Malaysian Mathematical Sciences Society, 2024-09, Vol.47 (5), Article 155</ispartof><rights>The Author(s) 2024</rights><rights>The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-d1314fd3958be7d6eef5c1ec4fcdc2ab9647b94a88be9816bd10eaf6192a57333</cites><orcidid>0000-0002-2321-6766</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40840-024-01747-8$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40840-024-01747-8$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Šumenjak, Tadeja Kraner</creatorcontrib><creatorcontrib>Tepeh, Aleksandra</creatorcontrib><title>Complexity of 2-Rainbow Total Domination Problem</title><title>Bulletin of the Malaysian Mathematical Sciences Society</title><addtitle>Bull. Malays. Math. Sci. Soc</addtitle><description>In this paper, we extend the findings of recent studies on
k
-rainbow total domination by placing our focus on its computational complexity aspects. We show that the problem of determining whether a graph has a 2-rainbow total dominating function of a given weight is NP-complete. This complexity result holds even when restricted to planar graphs. Along the way tight bounds for the
k
-rainbow total domination number of rooted product graphs are established. In addition, we obtain the closed formula for the
k
-rainbow total domination number of the corona product
G
∗
H
, provided that
H
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k
-rainbow total domination by placing our focus on its computational complexity aspects. We show that the problem of determining whether a graph has a 2-rainbow total dominating function of a given weight is NP-complete. This complexity result holds even when restricted to planar graphs. Along the way tight bounds for the
k
-rainbow total domination number of rooted product graphs are established. In addition, we obtain the closed formula for the
k
-rainbow total domination number of the corona product
G
∗
H
, provided that
H
has enough vertices.</abstract><cop>Singapore</cop><pub>Springer Nature Singapore</pub><doi>10.1007/s40840-024-01747-8</doi><orcidid>https://orcid.org/0000-0002-2321-6766</orcidid><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| subjects | Apexes Applications of Mathematics Complexity Graph theory Graphs Mathematics Mathematics and Statistics |
| title | Complexity of 2-Rainbow Total Domination Problem |
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