@MISC{Alvarez_eventriangulations, author = {Victor Alvarez}, title = {Even Triangulations of Planar Set of Points with Steiner Points}, year = {} }

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Abstract

Let P ⊂ R 2 be a set of n points of which k are interior points. Let uscallatriangulationT ofP even ifallits vertices have even degree, and pseudo-even if at least the k interior vertices have even degree. (Pseudo-) Even triangulations have one nice property; their vertices can be 3-colored, see [2, 3, 4]. Since one can easily check that for some sets of points, such triangulation do not exist, we show an algorithm that constructs a set S of at most ⌊(k +2)/3 ⌋ Steiner points (extra points) along with a pseudo-even triangulation T of P ∪S = V(T). 1