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On the rainbow connection of Cartesian products and their subgraphs
Klavžar, Sandi ; Mekiš, Gašper
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.
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