Problems in Topological Graph Theory Go to the Table of Contents Compiled by Dan Archdeacon List Started: August 5, 1995 Converted to the web: September 1, 1998 Last modified: November 15, 1998 E-Mail: dan.archdeacon@uvm.edu Postal Mail: Dan Archdeacon Dept. of Math. and Stat. University of Vermont Burlington VT 05401-1455 USA Abstract Do you think you've got problems I know I do. This paper ...

Open problems and conjectures concerning the determination of properties of families of graphs.

Problems These are problems which have been on my homepage and are now put out to grass. See also permutation group problems. 1. In 1956, Rudin defined a permutation of the integers which maps 3x to 2x, 3x+1 to 4x+1, and 3x-1 to 4x-1 for all x. Problem: Determine the cycle structure of this permutation. I have just learned (December 1998) that this problem is older: it is the original Collatz ...

Graph Theory Open Problems Index of Problems Unit Distance Graphs---chromatic number Unit Distance Graphs---girth Barnette's Conjecture Crossing Number of K(7, 7) Vertices and Neighbors on a Cycle Square of an Oriented Graph Unit Distance Graphs---chromatic number RESEARCHER: Robert Hochberg OFFICE: CoRE 414 Email:hochberg@dimacs.rutgers.edu DESCRIPTION: How many colors are needed so that if each ...