On Even Triangulations of 2-Connected Embedded Graphs
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by Huaming Zhang, Xin He
http://www.cse.buffalo.edu/tech-reports/2002-13.ps
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Abstract:
Recently, Homann 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 theorem, Homann and Kriegel signicantly 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. Homann and Kriegel conjectured that there is an O(n
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