2014/09/18 by Gabriela Araujo‐Pardo, Araujo-Pardo, Gabriela, Isabel Hubard +5
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1409.5175
openalex publication_date 2014/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Every n-edge colored n-regular graph G naturally gives rise to a simple abstract n-polytope, the colorful polytope of G, whose 1-skeleton is isomorphic to G. The paper describes colorful polytope versions of the associahedron and cyclohedron. Like their classical counterparts, the colorful associahedron and cyclohedron encode triangulations and flips, but now with the added feature that the diagonals of the triangulations are colored and adjacency of triangulations requires color preserving flips. The colorful associahedron and cyclohedron are derived as colorful polytopes from the edge colored graph whose vertices represent these triangulations and whose colors on edges represent the colors of flipped diagonals.