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A Lower Bound on the Diameter of the Flip Graph

2015/08/14 by Fabrizio Frati, Frati, Fabrizio
Computer Science · Mathematics · #Combinatorics (math.CO) #Computational Geometry (cs.CG) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #cs.CG #cs.DS #math.CO

paper · pdf · doi:10.48550/arxiv.1508.03473

arxiv created 2015/08/14 · arxiv updated 2015/08/17

Abstract

The flip graph is the graph whose nodes correspond to non-isomorphic combinatorial triangulations and whose edges connect pairs of triangulations that can be obtained one from the other by flipping a single edge. In this note we show that the diameter of the flip graph is at least (7n)/(3) + Θ(1), improving upon the previous 2n + Θ(1) lower bound.

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