Some bipartite Hamilton decomposable graphs that are regular of degree δ ≡ 2 (mod 4) are shown to have Hamilton decomposable line graphs. One consequence is that every bipartite Hamilton decomposable graph G with connectivity κ(G) = 2 has a Hamilton decomposable line graph L(G).

We extend Hamilton–Jacobi theory to Lagrange–Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints. We refer to the generalized Hamilton–Jacobi equation as the Dirac–Hamilton–Jacobi equation. For non-degenerate Lagrangian systems with nonholonomic constraints, the th...

Multiple edge-disjoint Hamilton cycles have been obtained in labelled star graphs Stn of degree n-1, using number-theoretic means, as images of a known base 2-labelled Hamilton cycle under label-mapping automorphisms of Stn. However, no optimum bounds for producing such edge-disjoint Hamilton cycles have been given, and no positive or negative results exist on whether Hamilton decompositions ca...

A graph G is 1-Hamilton-connected if G − x is Hamilton-connected for every vertex x ∈ V (G). In the paper we introduce a closure concept for 1-Hamiltonconnectedness in claw-free graphs. If G is a (new) closure of a claw-free graph G, then G is 1-Hamilton-connected if and only if G is 1-Hamilton-connected, G is the line graph of a multigraph, and for some x ∈ V (G), G − x is the line graph of a ...

A graph G is 1-Hamilton-connected if G − x is Hamilton-connected for every x ∈ V (G), and G is 2-edge-Hamilton-connected if the graph G + X has a hamiltonian cycle containing all edges of X for any X ⊂ E+(G) = {xy| x, y ∈ V (G)} with 1 ≤ |X| ≤ 2. We prove that Thomassen’s conjecture (every 4-connected line graph is hamiltonian, or, equivalently, every snark has a dominating cycle) is equivalent...

M. Warsi, D. W. Molloy, T. Standish, G. Wardlaw, and M. D. Noseworthy School of Biomedical Biomedical Engineering, McMaster University, Hamilton, Ontario, Canada, Medicine, St. Peters Hospital, Hamilton, Ontario, Canada, Medical Physics and Applied Radiation Sciences, McMaster University, Hamilton, Ontario, Canada, Electrical and Computer Engineering, School of Biomedical Engineering, McMaster ...

A. Fatemi-Ardekani, M. D. Noseworthy, and C. Boylan Medical Physics and Applied Radiation Sciences, McMaster University, Hamilton, Ontario, Canada, Brain-Body Institute, St. Joseph's Healthcare, Hamilton, Ontario, Canada, Electrical and Computer Engineering, School of Biomedical Engineering, McMaster University, Hamilton, Ontario, Canada, Diagnostic Imaging, St. Joseph's Healthcare, Hamilton, O...