The notorious middle two levels problem is to find a Hamilton cycle in the middle two levels, M2k+1, of the Hasse diagram of B2k+1 (the partially ordered set of subsets of a 2k + 1-element set ordered by inclusion). Previously, the best known result, due to Moews and Reid [11] in 1990, was that M2k+1 is Hamiltonian for all positive k through k = 11. We show that if a Hamilton path between two d...

Let G = Gn(a1, a2, ..., ak) denote a directed circulant graph of order n with k pairwise distinct jumps [1]. Antidirected Hamilton cycle in G is a cycle of n arcs that does not contain induced directed path P2. Let C 1 G, C 2 G, ..., C k G be pairwise arc-disjoint antidirected Hamilton cycles in G, each composed of exactly two distinct jumps. We give the necessary and sufficient conditions for ...

We consider a model of optimal investment and consumption with both habit-formation and partial observations in incomplete Itô processes markets. The individual investor develops addictive consumption habits gradually while he can only observe the market stock prices but not the instantaneous rates of return, which follow Ornstein-Uhlenbeck processes. Applying the Kalman-Bucy filtering theorem ...

It is shown that every connected vertex-transitive graph of order 4p, where p is a prime, is hamiltonian with the exception of the Coxeter graph which is known to possess a Hamilton path. In 1969, Lovász [22] asked if every finite, connected vertex-transitive graph has a Hamilton path, that is, a path going through all vertices of the graph. With the exception of K 2 , only four connected verte...

We first consider the following problem. We are given a fixed perfect matching M of [n] and we add random edges one at a time until there is a Hamilton cycle containing M . We show that w.h.p. the hitting time for this event is the same as that for the first time there are no isolated vertices in the graph induced by the random edges. We then use this result for the following problem. We genera...

In 1857, the Irish mathematician Sir William Hamilton(1805-1865) invented a game of travelling around the edges of a graph from vertex to vertex. Hamilton described the game, in a letter to his friend Graves, as a mathematical game on the dodecahedron in which one person sticks five pins in any five consecutive vertices and the other is required to complete the path to form a spanning cycle. In...

We show that deadlocks due to dependencies on consumption channels is a fundamental problem in mul ticast wormhole routing This issue of deadlocks has not been addressed in many previously proposed multicast algo rithms We also show that deadlocks on consumption chan nels can be avoided by using multiple classes of consump tion channels and restricting the use of consumption chan nels by multic...

Abstract Flight path optimization is designed for minimizing aircraft noise, fuel consumption and air pollution around airports. This paper gives theoretical considerations and algorithms solving the Hamilton-JacobiBellman equation (HJB) of aircraft trajectory optimization. Comparisons with direct and indirect methods are carried out. The OCP problem is transformed into new equalities-constrain...

We consider reaction-diffusion systems that can be out of equilibrium. In the preceding article a path integral formation of the Hamilton–Jacobi approximation of the Master equation of such systems. Using this path integral formulation, it is possible to calculate rate constants for the transition from one well to another well of the information potential and to give estimates of mean exit time...