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On the chromatic number of some flip graphs

Abstract : This paper studies the chromatic number of the following four flip graphs (under suitable definitions of a flip): the flip graph of perfect matchings of a complete graph of even order, the flip graph of triangulations of a convex polygon (the associahedron), the flip graph of non-crossing Hamiltonian paths of a set of points in convex position, and the flip graph of triangles in a convex point set. We give tight bounds for the latter two cases and upper bounds for the first two.
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Ruy Fabila-Monroy, David Flores-Peñaloza, Clemens Huemer, Ferran Hurtado, Jorge Urrutia, et al.. On the chromatic number of some flip graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2009, 11 (2), pp.47--56. ⟨hal-00988210⟩

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