573 KB54 KB200820252015Alspach, Brianštevilka:1letnik:8str. 35-53COBISSID:17368153ISSN:1855-3966URN:URN:NBN:SI:doc-6LOAEB73enUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneaCayley graphCayleyjev grafCoxeter groupCoxeterjeva grupaHamilton pathHamilton-connectedHamilton-laceableHamiltonova pothamiltonsko povezanhamiltonsko prepletenHamilton paths in Cayley graphs on Coxeter groups: I|We consider several families of Cayley graphs on the finite Coxeter groups ?$A_n$?, ?$B_n$?, and ?$D_n$? with regard to the problem of whether they are Hamilton-laceable or Hamilton-connected. It is known that every connected bipartite Cayley graph on ?$A_n$?, ?$n \ge 2$?, whose connection set contains only transpositions and has valency at least three is Hamilton-laceable. We obtain analogous results for connected bipartite Cayley graphs on ?$B_n$?, and for connected Cayley graphs on ?$D_n$?. Non-bipartite examples arise for the latter familyObravnavamo več družin Cayleyjevih grafov končnih Coxeterjevih grup ?$A_n$?, ?$B_n$? in ?$D_n$? glede na problem, ali so hamiltonsko prepletene ali hamiltonsko povezane. Znano je, da je vsak nepovezan dvodelen Cayleyev graf grupe ?$A_n$?, ?$n \ge 2$?, katerega množica povezav vsebuje samo transpozicije in ima valenco najmanj tri, hamiltonsko prepleten. Analogne rezultate dobimo za povezan dvodelen Cayleyev graf grup ?$B_n$?, in za povezane Cayleyeve grafe grup ?$D_n$?. Pri tej zadnji družini dobimo ne-dvodelne primereTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije