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...

A bent Hamilton cycle in a grid graph is one in which each edge in a successive pair of edges lies in a different dimension. We show that the d-dimensional grid graph has a bent Hamilton cycle if some dimension is even and d ≥ 3, and does not have a bent Hamilton cycle if all dimensions are odd. In the latter case, we determine the conditions for when a bent Hamilton path exists. For the d-dime...

F. Ruskey Joe Sawada y May 15, 2002 Abstra t A bent Hamilton y le in a grid graph is one in whi h ea h edge in a su essive pair of edges lies in a di erent dimension. We show that the d-dimensional grid graph has a bent Hamilton y le if some dimension is even and d 3, and does not have a bent Hamilton y le if all dimensions are odd. In the latter ase, we determine the onditions for when a bent ...

7Blake, J., Am. Jour. Med. Sci., 15, 63 (1848). 8 Marine, D., and Lenhart, C. H., Jour. Lab. Clin. Med., 3, 40 (1917). 9 Soley, M. H., and Hamilton, J. G., Proceedings, Sixth Pacific Science Congress (in press). 10 Hamilton, J. G., and Soley, M. H., Am. Jour. Physiol., 127, 557 (1939). 11 Hamilton, J. G., and Soley, M. H., Report submitted for publication. 12 Hamilton, J. G., and Soley, M. H., ...

A set S of edge-disjoint hamilton cycles in a graph G is said to be maximal if the edges in the hamilton cycles in S induce a subgraph H of G such that G EðHÞ contains no hamilton cycles. In this context, the spectrum SðGÞ of a graph G is the set of integersm such that G contains a maximal set of m edge-disjoint hamilton cycles. This spectrum has

We develop a discrete analogue of the Hamilton–Jacobi theory in the framework of the discrete Hamiltonian mechanics. We first reinterpret the discrete Hamilton–Jacobi equation derived by Elnatanov and Schiff in the language of discrete mechanics. The resulting discrete Hamilton– Jacobi equation is discrete only in time, and is shown to recover the Hamilton–Jacobi equation in the continuous-time...

A packing of a graph G with Hamilton cycles is a set of edgedisjoint Hamilton cycles in G. Such packings have been studied intensively and recent results imply that a largest packing of Hamilton cycles in Gn,p a.a.s. has size bδ(Gn,p)/2c. Glebov, Krivelevich and Szabó recently initiated research on the ‘dual’ problem, where one asks for a set of Hamilton cycles covering all edges of G. Our main...