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Full-Text Articles in Discrete Mathematics and Combinatorics
Facial Achromatic Number Of Triangulations With Given Guarding Number, Naoki Matsumoto, Yumiko Ohno
Facial Achromatic Number Of Triangulations With Given Guarding Number, Naoki Matsumoto, Yumiko Ohno
Theory and Applications of Graphs
A (not necessarily proper) k-coloring c : V(G) → {1,2,…k} of a graph G on a surface is a facial t-complete k-coloring if every t-tuple of colors appears on the boundary of some face of G. The maximum number k such that G has a facial t-complete k-coloring is called a facial t-achromatic number of G, denoted by ψt(G). In this paper, we investigate the relation between the facial 3-achromatic number and guarding number of triangulations on a surface, where a guarding number of a graph G embedded on a surface, …
On Flow Polytopes, Nu-Associahedra, And The Subdivision Algebra, Matias Von Bell
On Flow Polytopes, Nu-Associahedra, And The Subdivision Algebra, Matias Von Bell
Theses and Dissertations--Mathematics
This dissertation studies the geometry and combinatorics related to a flow polytope Fcar(ν) constructed from a lattice path ν, whose volume is given by the ν-Catalan numbers. It begins with a study of the ν-associahedron introduced by Ceballos, Padrol, and Sarmiento in 2019, but from the perspective of Schröder combinatorics. Some classical results for Schröder paths are extended to the ν-setting, and insights into the geometry of the ν-associahedron are obtained by describing its face poset with two ν-Schröder objects. The ν-associahedron is then shown to be dual to a framed triangulation of Fcar(ν), which is a …