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13.
Improved bounds for hypohamiltonian graphs
Goedgebeur, Jan, 1986- ; Zamfirescu, Carol T.
Graf ▫$G$▫ je hipohamiltonski če in samo če je ▫$G$▫ nehamiltonski in je ▫$G - v$▫ hamiltonski za vsak ▫$v \in V(G)$▫. V nadaljnjem za vsak graf privzamemo, da je hipohamiltonski. Aldred, Wormald in ...McKay so podali seznam vseh grafov reda največ 17. V članku predstavimo algoritem za generiranje vseh grafov danega reda in ga uporabimo za dokaz, da obstaja natanko 14 grafov reda 18 in 34 grafov reda 19. Razširimo tudi njihove rezultate v kubičnem primeru. Nadalje pokažemo, da velja: (i) najmanjši graf ožine 6 ima red 25, (ii) najmanjši ravninski graf ima red najmanj 23, (iii) najmanjši kubični ravninski graf ima red najmanj 54, in (iv) najmanjši kubični ravninski graf ožine 5 z netrivialno grupo avtomorfizmov ima red 78.
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