176 citations · 1.3k across the 156 of their papers we have counts for
6 papers · 1 filter
Graphoids
Neslihan Gügümcü, Louis H. Kauffman, Puttipong Pongtanapaisan
We study invariants of virtual graphoids, which are virtual spatial graph diagrams with two distinguished degree-one vertices modulo graph Reidemeister moves applied away from the…
On the orbits associated with the Collatz conjecture
Louis Kauffman, Pedro Lopes
This article is based upon previous work by Sousa Ramos and his collaborators. They first prove that the existence of only one orbit associated with the Collatz conjecture is equiv…
Edge colourings and topological graph polynomials
Joanna A. Ellis-Monaghan, Louis H. Kauffman, Iain Moffatt
A k-valuation is a special type of edge k-colouring of a medial graph. Various graph polynomials, such as the Tutte, Penrose, Bollobás-Riordan, and transition polynomials, admit co…
A State Calculus for Graph Coloring
Louis H. Kauffman
This paper discusses reformulations of the problem of coloring plane maps with four colors. We give a number of alternate ways to formulate the coloring problem including a tautolo…
Lune -- Free Knot Graphs
Shalom Eliahou, Frank Harary, Louis H. Kauffman
This paper is an exploration of simple four-regular graphs in the plane (i.e. loopless and with no more than one edge between any two nodes). Such graphs are fundamental to the the…
Reformulating the Map Color Theorem
Louis H. Kauffman
This paper discusses reformulations of the problem of coloring plane maps with four colors. The context is the edge-coloring with three colors of cubic graphs such that three disti…