| Naslov: | Domination of subcubic planar graphs with large girth |
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| Avtorji: | ID Cho, Eun-Kyung (Avtor)
ID Culver, Eric (Avtor)
ID Hartke, Stephen G. (Avtor)
ID Iršič Chenoweth, Vesna (Avtor) |
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| Datoteke: |  PDF - Predstavitvena datoteka, prenos (639,02 KB)
MD5: 5164ED1AF41B5B2529BBC72164929F38
 URL - Izvorni URL, za dostop obiščite https://amc-journal.eu/index.php/amc/article/view/3389
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| Jezik: | Angleški jezik |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: |  IMFM - Inštitut za matematiko, fiziko in mehaniko
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| Povzetek: | Since Reed conjectured in 1996 that the domination number of a connected cubic graph of order $n$ is at most $\lceil \frac13 n \rceil$, the domination number of cubic graphs has been extensively studied. It is now known that the conjecture is false in general, but Henning and Dorbec showed that it holds for graphs with girth at least $9$. Zhu and Wu stated an analogous conjecture for $2$-connected cubic planar graphs. In this paper, we present a new upper bound for the domination number of subcubic planar graphs: if $G$ is a subcubic planar graph with girth at least $8$, then $\gamma(G) < n_0 + \frac{3}{4} n_1 + \frac{11}{20} n_2 + \frac{7}{20} n_3$, where $n_i$ denotes the number of vertices in $G$ of degree $i$, for $i \in \{0,1,2,3\}$. We also prove that if $G$ is a subcubic planar graph with girth at least $9$, then $\gamma(G) < n_0 + \frac{13}{17} n_1 + \frac{9}{17} n_2 + \frac{6}{17} n_3$. |
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| Ključne besede: | graph theory, domination, subcubic planar graph, upper bound |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 01.01.2026 |
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| Leto izida: | 2026 |
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| Št. strani: | 32 str. |
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| Številčenje: | Vol. 26, no. 2, article no. P2.08 |
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| PID: | 20.500.12556/DiRROS-28409  |
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| UDK: | 519.17 |
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| ISSN pri članku: | 1855-3966 |
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| DOI: | 10.26493/1855-3974.3389.86c |
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| COBISS.SI-ID: | 225914883 |
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| Opomba: |
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| Datum objave v DiRROS: | 18.03.2026 |
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| Število ogledov: | 278 |
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| Število prenosov: | 139 |
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| Metapodatki: |    |
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