Unsolved problems presented at the Julius Petersen Graph Theory Conference

Unsolved problems presented at the Julius Petersen Graph Theory Conference

Unsolved Problems in Visibility Graph Theory

The visibility graph is a fundamental structure studied in the field of computational geometry, and pose some special challenges [12, 26]. Apart from theoretical interests, visibility graphs has important applications also. Some of the early applications include computing Euclidean shortest paths in the presence of obstacles [36] and decomposing two-dimensional shapes into clusters [40]. For mo...

Virtual Knot Theory – Unsolved Problems

Roger Fenn University of Sussex Department of Mathematics Sussex BN1 9RF, England [email protected] and Louis H. Kauffman Department of Mathematics, Statistics and Computer Science University of Illinois at Chicago 851 South Morgan St., Chicago IL 60607-7045, USA [email protected] and Vassily O. Manturov Moscow State University Department of Mechanics and Mathematics 119992, GSP-2,Leninskie Go...

Addressing the Petersen graph

Motivated by a problem on message routing in communication networks, Graham and Pollak proposed a scheme for addressing the vertices of a graph G by N -tuples of three symbols in such a way that distances between vertices may readily be determined from their addresses. They observed that N ≥ h(D), the maximum of the number of positive and the number of negative eigenvalues of the distance matri...

The ubiquitous Petersen graph

Chartrand, G., H. Hevia and R.J. Wilson, The ubiquitous Petersen graph, Discrete Mathematics 100 (1992) 303-311.