On realization graphs of degree sequences

Given the degree sequence $d$ of a graph, the realization graph of $d$ is the graph having as its vertices the labeled realizations of $d$, with two vertices adjacent if one realization may be obtained from the other via an edge-switching operation. We describe a connection between Cartesian products in realization graphs and the canonical decomposition of degree sequences described by R.I. Tyshkevich and others. As applications, we characterize the degree sequences whose realization graphs are triangle-free graphs or hypercubes.Comment: 10 pages, 5 figure

On connectedness and hamiltonicity of direct graph bundles

A necessary and sufficient condition for connectedness of direct graph bundles is given where the fibers are cycles. We also prove that all connected direct graph bundles $X=C_stimes^{alpha}C_t$ are Hamiltonian

Hamilton cycles in graph bundles over a cycle with tree as a fibre

AbstractA sufficient and necessary condition for the existence of a Hamilton cycle in a graph bundle with a cycle as a base and a tree as a fibre is obtained