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Drawing graphs on surfaces
Žitnik, Arjana
Graf, ki je celično vložen v neko orientabilno ploskev ▫$S$▫, lahko vedno narišemo v nek fundamentalni poligon ploskve ▫$S$▫ na tak način, da je rob poligona sestavljen iz povezav in točk grafa; ...lahko pa ga v nek fundamentalni poligon ploskve narišemo tudi na tak način, da so vse točke v notranjosti poligona in poljubna povezava prečka rob poligona kvečjemu enkrat. V članku poiščemo potrebna in zadostna pogoja, katerima mora zadoščati vložitev grafa na ploskev, da ga lahko narišemo na eden ali drugi način v standardni poligon ploskve, tj. poligon s simboličnim zapisom ▫$a_1b_1a_1^{-1}b_1^{-1} a_2b_2a_2^{-1} b_2^{-1}...$▫. Izpeljemo tudi algoritem, ki (v primeru, da obstaja) najde ustrezno reprezentacijo v standardnbi poligon ploskve. Za vsako ploskev ima algoritem polinomsko časovno zahtevnost.
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