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13.
On polyhedral embeddings of cubic graphs
Mohar, Bojan, 1956- ; Vodopivec, Andrej, 1978-
Ogledamo si obstoj poliedrskih vložitev kubičnih grafov pri nekaterih operacijah. Za nekaj znanih družin snarkov pokažemo, da nimajo poliedrskih vložitev v orientabilne ploskve. Ti rezultati ...podpirajo Grünbaumovo hipotezo, da noben snark nima poliedrske vložitve v orientabilno ploskev. Hipoteza je preverjena za grafe z do 30 točkami s pomočjo računalnika. Za vsako neorientabilno ploskev ▫$S$▫ konstruiramo kubičen graf, ki sa ga da poliedrsko vložiti v ▫$S$▫, a ni po povezavah 3-obarvljiv.
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