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13.
Overlap in consistent cycles
Miklavič, Štefko ; Potočnik, Primož, 1971- ; Wilson, Steve, matematik
(Usmerjeni) cikel ▫$C$▫ grafa ▫$\Gamma$▫ se imenuje konsistenten, če obstaja takšen automorfizem grafa ▫$\Gamma$▫, ki deluje na ▫$C$▫ kot rotacija za en korak. Dokaj neznan rezultat J. H. Conwaya ...trdi, da je v ločno tranzitivnem grafu stopnje ▫$d$▫ število ▫$Aut(\Gamma)$▫-orbit konsistentnih ciklov vedno enako ▫$d-1$▫. V tem članku posplošimo definicijo konsistentnih ciklov na ▫$\frac{1}{k}$▫-konsistentne cikle. Cikel ▫$C$▫ je ▫$\frac{1}{k}$▫-konsistenten, če obstaja takšen automorfizem grafa ▫$\Gamma$▫, ki deluje na ▫$C$▫ kot rotacija za ▫$k$▫ korakov. V članku ▫$\frac{1}{k}$▫-konsistentne cikle študiramo glede na njihovo prekrivanje. Na ta način dobimo enostaven dokaz Conwayevega rezultata, pa tudi njegovo posplošitev za število orbit ▫$\frac{1}{k}$▫-konsistentnih ciklov. Na koncu članka je podanih nekaj primerov.
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