Abstract:The prism over a graph G is the Cartesian product G K 2 of G with the complete graph K 2 . If the prism over G is hamiltonian, we say that G is prism-hamiltonian. We prove that triangulations of the plane, projective plane, torus, and Klein bottle are prism-hamiltonian. We additionally show that every 4-connected triangulation of a surface with sufficiently large representativity is prism-hamiltonian, and that every 3-connected planar bipartite graph is prism-hamiltonian.

This work examines the properties and mathematical structure of factorized time correlation (FTC) diagram analysis in a general context. The goal is to extract general principles and analytic behavior that are not tied to any particular phenomenon in physics. It is hoped that this will provide a basis for expanded use of FTC diagram analysis beyond its current employment in the study of noisy light-based nonlinear optical spectroscopy. Furthermore, the concept of indirect correlation in a two-channel system driven by twin stationary circular Gaussian stochastic inputs is defined and discussed both analytically and through FTC diagram analysis.

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We investigate the firefighter problem for regular infinite directed grids. We provide a complete classification of these grids by dividing them into two categories: grids where a single outbreak of fire can be contained with one firefighter per time step and grids that require a second firefighter at some time step. We then investigate infinite directed grids where the degrees of a single vertex are different from the degrees of all other vertices in the grid.