On the rainbow connection of Cartesian products and their subgraphsKlavžar, Sandi (Avtor) Mekiš, Gašper (Avtor) graph theoryrainbow connectionstrong rainbow connectionCartesian product of graphsisometric subgraphhypercubeRainbow 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.University of Zielona Góra20122017-03-31 14:16:54Znanstveno delo65350ISSN: 1234-3099UDK: 519.17OceCobissID: 7487065COBISS_ID: 16417369ISSN pri članku: 1234-3099NUK URN: URN:SI:UM:DK:5HDKVZY4sl