351 KB9 KB200820252019Guo, XiaYang, Yanštevilka:1letnik:16str. 19-24ISSN:1855-3966COBISSID_HOST:18699353URN:URN:NBN:SI:doc-9Y1AWR1RenUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporanea4-girth-thickness4-ožinska debelinacomplete tripartite graphdebelinapolni tridelni grafthicknessA note on the 4-girth-thickness of Ksub{n,n,n}|The 4-girth-thickness ?$\theta(4, G)$? of a graph ?$G$? is the minimum number of planar subgraphs of girth at least four whose union is ?$G$?. In this paper, we obtain that the 4-girth-thickness of complete tripartite graph ?$K_{n, n, n}$? is ?$\lceil\frac{n + 1}{2}\rceil$? except for ?$\theta(4, K_{1, 1, 1}) = 2$?. And we also show that the 4-girth-thickness of the complete graph ?$K_{10}$? is three which disprove the conjecture posed by C. Rubio-Montiel Ars Math. Contemp. 14, No. 2, 319--327 (2018) concerning to ?$\theta(4, K_{10})$?4-ožinska-debelina ?$\theta(4, G)$? grafa ?$G$? je minimalno število ravninskih podgrafov ožine najmanj štiri, katerih unija je ?$G$?. V članku pokažemo, da je 4-ožinska-debelina polnega tridelnega grafa ?$K_{n, n, n}$? enaka ?$\lceil\frac{n + 1}{2}\rceil$? razen za ?$\theta(4, K_{1, 1, 1}) = 2$?. Pokažemo tudi, da je 4-ožinska-debelina polnega grafa ?$K_{10}$? enaka tri, kar ovrže domnevo, ki jo je postavil Rubio-Montiel Ars Math. Contemp. 14, No. 2, 319--327 (2018) v zvezi z ?$\theta(4, K_{10})$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije