2017/01/27 by Satoshi Murai, Yusuke Suzuki, Murai, Satoshi +1
Mathematics · Computer Science · #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1701.08060
In this paper, we show that two balanced triangulations of a closed surface are not necessary connected by a sequence of balanced stellar subdivisions and welds. This answers a question posed by Izmestiev, Klee and Novik. We also show that two balanced triangulations of a closed surface are connected by a sequence of three local operations, which we call the pentagon contraction, the balanced edge subdivision and the balanced edge weld. In addition, we prove that two balanced triangulations of the 2-sphere are connected by a sequence of pentagon contractions and their inverses if none of them are octahedral spheres.