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13.
Systems of curves on surfaces
Juvan, Martin ; Malnič, Aleksander ; Mohar, Bojan, 1956-
V članku je dokazano, da za vsako kompaktno ploskev ▫$\Sigma$▫ in naravno število ▫$k$▫ obstaja taka konstanta ▫$N$▫, da je moč poljubne družine ▫$\Gamma$▫ paroma nehomotopnih sklenjenih krivulj na ...▫$\Sigma$▫, pri čemer se poljubni krivulji iz ▫$\Gamma$▫ sekata kvečjemu v ▫$k$▫ točkah, omejena z ▫$N$▫. Dokazano je tudi, da za vsako kompaktno ploskev obstaja le končno mnogo ▫$k$▫-minimalnih triangulacij in končno mnogo za celično širino ▫$k$▫-minimalnih vložitev.
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