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...

Classic, and Explicit Turnpikes Paolo Guasoni · Constantinos Kardaras · Scott Robertson · Hao Xing Received: date / Accepted: date Abstract Portfolio turnpikes state that, as the investment horizon increases, optimal portfolios for generic utilities converge to those of isoelastic utilities. This paper proves three kinds of turnpikes. In a general semimartingale setting, the abstract turnpike s...

Author details Department of Clinical Epidemiology & Biostatistics, McMaster University, 501-25 Charlton Avenue East, Hamilton, ON L8N 1Y2, Canada. St. Joseph’s Healthcare Hamilton, McMaster University, 501-25 Charlton Avenue East, Hamilton, ON L8N 1Y2, Canada. Department of Medicine, McMaster University, Hamilton, ON, Canada. Interdepartmental Division of Critical Care, Hamilton Health Science...

A Hamilton circle in an infinite graph is a homeomorphic copy of the unit circle S1 that contains all vertices and all ends precisely once. We prove that every connected, locally connected, locally finite, claw-free graph has such a Hamilton circle, extending a result of Oberly and Sumner to infinite graphs. Furthermore, we show that such graphs are Hamilton-connected if and only if they are 3-...

We study M-alternating Hamilton paths, and M-alternating Hamilton cycles in a simple connected graph G on ν vertices with a perfect matchingM . Let G be a bipartite graph, we prove that if for any two vertices x and y in different parts of G, d(x)+d(y) ≥ ν/2+2, then G has an M-alternating Hamilton cycle. For general graphs, a condition for the existence of an M-alternating Hamilton path startin...