| Naslov: | On k-rainbow total domination and a related conjecture |
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| Avtorji: | ID Erveš, Rija (Avtor)
ID Kraner Šumenjak, Tadeja (Avtor)
ID Tepeh, Aleksandra (Avtor) |
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| Datoteke: |  s40840-026-02060-2.pdf (367,71 KB)
MD5: AB2F763022F9F533F7A0D78D75866762
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Članek v reviji |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | FGPA - Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo
FERI - Fakulteta za elektrotehniko, računalništvo in informatiko
FKBV - Fakulteta za kmetijstvo in biosistemske vede
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| Opis: | A k-rainbow total dominating function of a graph G is a function f : V(G) → 2[k] such that for every vertex v ∈ V(G) with f (v) = ∅, the union of the colors assigned to its neighbors equals [k], and if f (v) = {i}, then v has a neighbor u with i ∈ f (u). The minimum weight of such a function is called the k-rainbow total domination number of G and is denoted by γkrt(G). We contribute to the study of k-rainbow total domination by proving one conjecture and constructing a counterexample to another. First, we show that the problem of determining whether a graph admits a k-rainbow total dominating function of a given weight is NP-complete. In the second part, we derive an upper bound on the domination number of a graph G in terms of γkrt(G) and the frequency of the least-used color in a k-rainbow total dominating function. This result not only provides an alternative and shorter proof of a known lower bound on γkrt(G)/γ (G), originally established by Ojakian et al. (2021), but also contributes to disproving their conjecture on the lower bound for γkrt(G) when k = 4. |
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| Ključne besede: | dominaiton, rainbow total domination, NP-complete |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Poslano v recenzijo: | 23.06.2025 |
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| Datum sprejetja članka: | 03.02.2026 |
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| Datum objave: | 19.02.2026 |
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| Založnik: | Springer |
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| Leto izida: | 2026 |
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| Št. strani: | 114 str. |
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| Številčenje: | Vol. 49, [article no.] 62 |
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| PID: | 20.500.12556/DKUM-97220  |
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| UDK: | 51 |
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| COBISS.SI-ID: | 269154307 |
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| DOI: | 10.1007/s40840-026-02060-2 |
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| ISSN pri članku: | 2180-4206 |
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| Avtorske pravice: | © The Author(s) 2026 |
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| Datum objave v DKUM: | 24.02.2026 |
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| Število ogledov: | 98 |
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| Število prenosov: | 7 |
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| Metapodatki: |    |
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| Področja: | Ostalo
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