20.500.12556/DKUM-65350 On the rainbow connection of Cartesian products and their subgraphs O mavrični povezanosti kartezičnih produktov in njihovih podgrafov Rainbow connection number of Cartesian products and their subgraphs are considered. Previously known bounds are compared and non-existence of such bounds for subgraphs of products are discussed. It is shown that the rainbow connection number of an isometric subgraph of a hypercube is bounded above with the rainbow connection number of the hypercube. Isometric subgraphs of hypercubes with the rainbow connection number smaller as much as possible than the rainbow connection of the hypercube are constructed. The concept of c-strong rainbow coloring is introduced. In particular it is proved that the so-called ▫$\Theta$▫-coloring of an isometric subgraph of a hypercube is its unique optimal c-strong rainbow coloring. Obravnavana je mavrična povezanost kartezičnega produkta grafov in podgrafov tega produkta. Primerjane so že od prej znane meje in obravnavan je neobstoj takih mej za podgrafe produkta. Pokazano je, da je mavrična povezanost izometričnega podgrafa hiperkocke navzgor omejena z mavrično povezanostjo hiperkocke. Konstruirani so izometrični podgrafi hiperkocke s čim manjšo mavrično povezanostjo glede na mavrično povezanost hiperkocke. Vpeljan je pojem c-krepkega mavričnega barvanja. Dokazano je, da je t.i. ▫$\Theta$▫-barvanje izometričnega podgrafa hiperkocke edino optimalno c-krepko mavrično barvanje. graph theory rainbow connection strong rainbow connection Cartesian product of graphs isometric subgraph hypercube teorija grafov mavrična povezanost krepka mavrična povezanost kartezični produkt grafov izometrični podgraf hiperkocka true true true University of Zielona Góra Angleški jezik Slovenski jezik Znanstveno delo 2017-03-31 14:16:54 2017-03-31 14:17:35 2026-03-27 09:50:34 2019-07-11 15:15:27 2012 0 0 str. 783-793 št. 4 Letn. 32 2012 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2011-06-08 2012-02-06 0000-00-00 1234-3099 519.17 7487065 16417369 1234-3099 URN:SI:UM:DK:5HDKVZY4 Discussiones_Mathematicae_Graph_Theory_2012_Klavzar,_Mekis_On_the_rainbow_connection_of_Cartesian_products_and_their_subgraphs.pdf Discussiones_Mathematicae_Graph_Theory_2012_Klavzar,_Mekis_On_the_rainbow_connection_of_Cartesian_products_and_their_subgraphs.pdf 1 08E030D2D9C851DDED1D3C0708735260 cd7d3bacbc40f720f01302c08ebb8207d13e14213f61c4a748e3e17dfd34c68f 0bd90d98-7c0e-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=110427 http://www.discuss.wmie.uz.zgora.pl/gt/index.php?doi=10.7151/dmgt.1644 1 https://dk.um.si/Dokument.php?lang=slv&id=110426 Fakulteta za naravoslovje in matematiko 0 0 0