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Generating locally cyclic triangulations of surfaces
Malnič, Aleksander ; Mohar, Bojan, 1956-
Lokalno-cikličen graf je povezan graf z lastnostjo, da je za vsako vozlišče inducirani podragraf na sosedih izomorfen ciklu. Ti grafi so v bijektivni korespondenci z lokalno cikličnimi ...triangulacijami sklenjenih ploskev, t.j. triangulacijami za katere je vsak cikel dolžine ▫$B$▫ celica. Vse lokalno ciklične triangulacije dane sklenjene ploskve ▫$S$▫ se dajo zgenerirati iz neke minimalne podmnožice ▫$B(S)$▫ s pomočjo ekspanzije vozlišča v povezavo kot generativnim pravilom. V članku je dokazano, da je minimalna množica ▫$B(S)$▫ končna za vsako orientabilno sklenjeno ploskev. Pokazano je, kako se da osnovni izrek uporabiti pri študiju hipoteze o dvojnem cikličnem pokritju 2-povezanih grafov.
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