7 papers
Some properties of Bowlin and Brin's color graphs
Rui Pedro Carpentier, Roger Picken
Bowlin and Brin defined the class of color graphs, whose vertices are triangulated polygons compatible with a fixed four-coloring of the polygon vertices. In this article it is pro…
Extending triangulations of the 2-sphere to the 3-disk preserving a 4-coloring
Rui Pedro Carpentier
In this paper we prove that any triangulation of a 2-dimensional sphere with a strict 4-coloring on its vertices can seen as the boundary of a triangulation of a 3-dimensional disk…
Three-Colorings of Cubic Graphs and Tensor Operators
Rui Pedro Carpentier
Penrose's work \cite{8} established a connection between the edge 3-colorings of cubic planar graphs and tensor algebras. We exploit this point of view in order to get algebraic re…
On signed diagonal flip sequences
Rui Pedro Carpentier
Eliahou \cite{2} and Kryuchkov \cite{9} conjectured a proposition that Gravier and Payan \cite{4} proved to be equivalent to the Four Color Theorem. It states that any triangulatio…
Representations of non-singular planar tangles by operators
Rui Pedro Carpentier
In this paper we study how to distinguish two embeddings of a finite collection of disjoint circles into the plane up to planar isotopy. We adopt the spirit of the approach by V. T…
Topological notions for Kauffman and Vogel's polynomial
Rui Pedro Carpentier
In [2] Kauffman and Vogel constructed a rigid vertex regular isotopy invariant for unoriented four-valent graphs embedded in three dimensional space. It assigns to each embedded gr…