Hamilton paths in Cayley graphs on Coxeter groups: I
Alspach, Brian
Obravnavamo 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 primere.
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