166 KB5 KB200820262026Cho, Eun-KyungCulver, EricHartke, Stephen G.Iršič Chenoweth, Vesnaštevilka:2, article p2.08letnik:2632 str.DOI:10.26493/1855-3974.3389.86cISSN:1855-3966COBISSID_HOST:225914883URN:URN:NBN:SI:doc-UZHA5QN6enUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneadominationgraph theorysubcubic planar graphupper boundDomination 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 ?$\gamma(G) < n_0 + \frac{13}{17} n_1 + \frac{9}{17} n_2 + \frac{6}{17} n_3$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije