Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs
Potočnik, Primož, 1971- ; Spiga, Pablo ; Verret, Gabriel
Slavni Tuttov izrek pravi, da je red vozliščnega stabilizatorja v povezanem 3-valentnem ločno-tranzitivnem grafu ne preseže vrednosti 48. Dolgo je bilo znano, da ta izrek ne velja v širšem kontekstu ...povezanih 3-valentnih vozliščno-tranzitivnih grafov. Znanih je bilo več družin takšnih grafov, v katerih red stabilizatorja raste eksponentno. V članku dokažemo presenetljiv rezultat, ki pravi, da je z izjemo teh dobro znanih družin, red vozliščnega stabilizatorja v povezanem 3-valentnem vozliščno tranzitivnem grafu omejen s sublinearno funkcijo reda grafa.
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