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Eulerjevi sprehodi s predpisanimi zavoji : doktorska disertacijaŽitnik, ArjanaEulerjeve obhode v grafih na ploskvah, pri katerih poljubni dve zaporedni povezavi ležita na meji skupnega lica, imenujemo A-obhodi. Delo obravnava A-obhode v grafih, ki so vloženi v orientabilne ... ploskve. Na orientiranih ploskvah je pri potovanju vzdolž sklenjene krivulje mogoče definirati pojem leve in desne strani. Tako lahko pri potovanju vzdolž A-obhoda povemo, ali smo za naslednjo povezavo izbrali povezavo desno ali levo od povezave, po kateri smo prišli v vozlišče. Zaporedje zavojev vzdolž A-obhoda potem označimo z zaporedjem znakov L (levo) in D (desno). V tretjem poglavju obravnavamo Petriejeve obhode, pri katerih izmenično zavijamo levo in desno. V četrtem poglavju karakteriziramo grafe v ravnini, ki imajo A-obhod z danim zaporedjem zavojev ▫$z$▫. Izbranemu A-obhodu ustreza več različnih zaporedij zavojev, ki jih vsa štejemo za ekvivalentna. Ustrezen ekvivalenčni razred označimo z ▫$[z]$▫ in pravimo, da je A-obhod tipa ▫$[z]$▫. Pri tem je tip ▫$[z]$▫ podan samo s periodo. Iz karakterizacije dobimo tudi algoritem za konstrukcijo grafov z A-obhodom tipa ▫$[z]$▫. Na koncu obravnavamo problem zaporedno-vzporedne razširitve grafov v ravnini do grafov z Eulerjevim Petriejevim obhodom. Več posebnih primerov razširitev prevedemo na problem iskanja Hamiltonovega cikla, ki je že precej raziskan.Type of material - dissertation ; adult, seriousPublication and manufacture - Ljubljana : [A. Žitnik], 2001Language - slovenianCOBISS.SI-ID - 11261529
Author
Žitnik, Arjana
Other authors
Pisanski, Tomaž
Topics
Teorija grafov |
Disertacije |
Eulerjevi grafi |
Disertacije |
grafi na ploskvah |
vložitve grafov |
A-obhodi |
Petriejevi sprehodi |
sprehodi levo-desno |
graf rdečih lic |
hipergraf rdečih lic |
konstrukcije grafov |
algoritmi
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Žitnik, Arjana | 14273 |
Pisanski, Tomaž | 01941 |
Source: Personal bibliographies
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