The prism over a graph G is the Cartesian product G2K2 of G with the complete graph K2. If G is hamiltonian, then G2K2 is also hamiltonian but the converse does not hold in general. Having a hamiltonian prism is shown to be an interesting relaxation of being hamiltonian. In this paper, we examine classical problems on hamiltonicity of graphs in the context of having a hamiltonian prism. c © ???...

This document contains a proof of the Cayley-Hamilton theorem based on the development of matrices in HOL/Multivariate Analysis.

The Adams apportionment method is the only divisor method that consistently favors small districts relative to the Hamilton method. The Jefferson method is the only divisor method that favors large districts relative to the Hamilton method. These statements hold for the Balinski and Young [3] interpretation of "favoring small/large districts," and for the partial "majorization ranking" introduc...

BHF Glasgow Cardiovascular Research Centre, University of Glasgow, Glasgow, Scotland, UK AstaZeneca R&D, Mölndal, Sweden Department of Medicine, Karolinska University Hospital, Solna, Stockholm, Sweden AstraZeneca LP, Wilmington, DE, USA Duke University Medical Center, Durham, NC, USA HGM-McMaster Clinic, Hamilton, Ontario, Canada Department of Emergency and Cardiovascular Medicine, Sahlgrenska...

In the first part of the thesis we define an automorphism φn for each star graph Stn of degree n − 1, which yields permutations of labels for the edges of Stn taken from the set of integers {1, . . . , bn/2c}. By decomposing these permutations into permutation cycles, we are able to identify edge-disjoint Hamilton cycles that are automorphic images of a known two-labelled Hamilton cycle H1 2(n)...