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Surface triangulations with isometric boundary
Fisk, Steve ; Mohar, Bojan, 1956-
Triangulacija ▫$T$▫ ploskve ▫$S$▫ z robom ▫$\partial S$▫ je izometrična, če je grafovska razdalja med poljubnima točkama ▫$x,y$▫ na isti komponenti ▫$\partial S$▫ v celem grafu ▫$T$▫ enaka razdalji ...med ▫$x$▫ in ▫$y$▫ v ▫$T\cap \partial S$▫. Če je ▫$T$▫ izometrična triangulacija diska, tedaj je pokazano, da je ▫$|V(T|=\Omega (n^2)$▫, kjer je ▫$n$▫ število točk na robu. Izometrična triangulacija je ireducibilna, če stisnitev poljubne povezave da neizometrično triangulacijo ali pa spremeni ploskev. Dokazano je, da ima vsaka ploskev ▫$S$▫ le končno mnogo ireducibilnih triangulacij z danim številom ▫$n$▫ točk na robu.
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