20.500.12556/DiRROS-28409 Domination of subcubic planar graphs with large girth 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 $\gamma(G) < n_0 + \frac{13}{17} n_1 + \frac{9}{17} n_2 + \frac{6}{17} n_3$. graph theory domination subcubic planar graph upper bound true false true Angleški jezik Ni določen Neznano 2026-03-18 14:09:21 2026-03-18 14:09:22 2026-03-25 03:44:45 0000-00-00 00:00:00 2026 0 0 32 str. no. 2, article no. P2.08 Vol. 26 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2026-01-01 519.17 1855-3966 10.26493/1855-3974.3389.86c 225914883 amc_3389.pdf amc_3389.pdf 1 5164ED1AF41B5B2529BBC72164929F38 656d314fcfbb9ff730ad4a336e1fffbee8fbb97916abccbb65cf3730e65c67a6 1d2f2608-22cc-11f1-a33f-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=42036 https://amc-journal.eu/index.php/amc/article/view/3389 1 b099156f-22cb-11f1-a33f-001a4af901a5 https://dirros.openscience.si/Dokument.php?lang=slv&id=42032 Inštitut za matematiko, fiziko in mehaniko 0 0 0