Abstract
Graphs and Algorithms 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.
Highlights
To cite this version: Ruy Fabila-Monroy, David Flores-Peñaloza, Clemens Huemer, Ferran Hurtado, Jorge Urrutia, et al
This paper studies the chromatic number of the following four flip graphs:
This paper studies the chromatic number of some flip graphs
Summary
(2) Every adjacent pair in D1 together with its neighborhood in H1 induces a K4 in Gn. For extending an n-coloring of H0 to one of H1 we use the two properties of Gn. (2) Every adjacent pair in D1 together with its neighborhood in H1 induces a K4 in Gn Both properties follow because, on one hand, flipping an edge of Γ1 that is in the convex hull of Sn yields a path in D2. 2 in Hi. The first property follows because, on one hand, flipping an edge of Γi that is in the convex hull of Sn yields a path in Di+1. On the other hand, flipping an edge of Γ that is not in the convex hull of Sn yields a path in Di−1.
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