20.500.12556/DKUM-62610 Dekompozicija kartezičnega produkta regularnih grafov v izomorfna drevesa Decomposition of cartesian products of regular graphs into isomorphic trees Diplomsko delo obravnava družine 2m-regularnih grafov in m-regularnih dvodelnih grafov, ki se dekomponirajo v izomorfne kopije drevesa T z m povezavami. Obravnavana je k-terica r1,..., rk z vsoto i=1 do k ri = m. Za drevo T s takim k-barvanjem po povezavah z r i povezavami barve i, da ima vsaka pot v T eno ali dve povezavi iste barve, je predstavljen rezultat, da se vsak kartezični produkt grafov G1,...,Gk, kjerje Gi 2ri-regularen graf za 1 <= i <= k, dekomponira v kopije drevesa T. The diploma paper discesses the families of 2m-regular graphs and m-regular bipartite graphs that are known to decompose into isomorphic copies of a tree T with m edges. A k-tuple r1,...,rk with i=1 k ri=m. Is considered k-edge-coloring with ri edges of color i, such that every path in T use some color once or twice. For a tree containing the result that every cartesian product of graphs G1,..., Gk, such that Gi is 2ri-regular for 1 <= i <= k, decomposes into copies of T is presented. dekompozicijski izrek dobro barvanje drevesa kartezični produkt decomposition theorem edge-colorings trees Cartesian product true true false [G. Maučec] Slovenski jezik Angleški jezik Diplomsko delo 2016-08-30 07:15:30 2016-11-11 13:56:56 2022-06-29 03:09:20 2019-07-11 13:01:24 2016 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.174(043.2) 22722568 URN:SI:UM:DK:LCB0Y9KQ UN_Maucec_Gregor_2016.pdf UN_Maucec_Gregor_2016.pdf 1 18BAB6E7FC0D4F5B07EEBEFDA237742A 528fe8dbab560e244789dbc9401558df5e15dbae63f831e3d3744b7752758172 b26cd0a9-7c0d-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=106857 Fakulteta za naravoslovje in matematiko 0 0 0