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13.
Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphisms
Marušič, Dragan
Domneva se, da grupa avtomorfizmov točkovno tranzitivnih (di)grafov, in splošneje 2-zaprtje tranzitivnih permutacijskih grup, vsebuje element brez negibnih točk, katerega red je praštevilo, in torej ...premore od identitete različen element, katerega orbite imajo vse enako dolžino, ali, kot takemu elementu pravimo, polregularen element. Znane potrditve te domneve za grafe s primitivnimi in kvaziprimitivnimi grupami avtomorfizmov dajejo slutiti, da je ključ do popolne rešitve tega problema treba iskati v rešljivih grupah. Namen tega članka je predstaviti pregled znanih rezultatov in predlagati možne nadaljnje smeri raziskav, ki utegnejo voditi k popolni rešitvi problema.
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