| Title: | Domination of subcubic planar graphs with large girth |
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| Authors: | ID Cho, Eun-Kyung (Author)
ID Culver, Eric (Author)
ID Hartke, Stephen G. (Author)
ID Iršič Chenoweth, Vesna (Author) |
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| Files: |  PDF - Presentation file, download (639,02 KB)
MD5: 5164ED1AF41B5B2529BBC72164929F38
 URL - Source URL, visit https://amc-journal.eu/index.php/amc/article/view/3389
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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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| Keywords: | graph theory, domination, subcubic planar graph, upper bound |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.01.2026 |
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| Year of publishing: | 2026 |
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| Number of pages: | 32 str. |
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| Numbering: | Vol. 26, no. 2, article no. P2.08 |
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| PID: | 20.500.12556/DiRROS-28409  |
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| UDC: | 519.17 |
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| ISSN on article: | 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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| Note: |
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| Publication date in DiRROS: | 18.03.2026 |
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| Views: | 275 |
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| Downloads: | 138 |
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| Metadata: |    |
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