Abstract
Recently, Hoffmann and Kriegel proved an important combinatorial theorem [4]:Every 2-connected bipartite plane graph G has a triangulation in which all vertices have even degree (it’s called an even triangulation.Combined with a classical Whitney’s Theorem,this result implies that every such a graph has a 3-colorable plane triangulation.Using this result, Hoffmann and Kriegel significantly improved the upper bounds of several art gallery and prison guard problems.A complicated O(n 2) time algorithm was obtained in [4] for constructing an even triangulation of G Hoffmann and Kriegel conjectured that there is an O(n3/2) algorithm for solving this problem [4]. In this paper,we develop a very simple O(n) time algorithm for solving this problem.Our algorithm is based on thorough study of the structure of all even triangulations of G. We also obtain a simple formula for computing the number of distinct even triangulations of G
Research supported in part by N F Grant CCR-9912418.
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Zhang, H., He, X. (2002). A Simple Linear Time Algorithm for Finding Even Triangulations of 2-Connected Bipartite Plane Graphs. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_78
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DOI: https://doi.org/10.1007/3-540-45749-6_78
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