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13.
Odd complete minors in even embeddings on surfaces
Fijavž, Gašper ; Nakamoto, Atsuhiro
V članku obravnavamo problem lihih ▫$K_m$▫-minorjev v sodih vložitvah grafov v ploskve. V prvem delu predstavimo splošen rezultat o ▫$K_m$▫-minorju v sodi vložitvi. Pri izbranem naravnem številu ...▫$m$▫ pokažemo, da z vsako ploskev ▫$F^2$▫ zadosti velikega roda obstaja konstanta ▫$N=N(F^2)$▫ pri kateri vsaka soda vložitev v ▫$F^2$▫ s celično širino vsaj ▫$N$▫ vsebuje lihi ▫$K_m$▫-minor. V preostanku pa pokažemo, da vsaka soda vložitev v poljubno orientabilno ploskev s celično širino vsaj 19 vsebuje lihi ▫$K_5$▫-minor.
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