In this paper, we introduce two new algorithm to find a Hamilton Circuit in a graph G = (V, E). One algorithm is use a multistage graph as a special NFAs to find all Hamilton Circuit in exponential time; while another is use O(|V|) variant multistage graph as a special state set NFAs to find a fuzzy data of all Hamilton Circuit in polynomial time. The fuzzy data of the data contain those data, ...

The problem of packing Hamilton cycles in random and pseudorandom graphs has been studied extensively. In this paper, we look at the dual question of covering all edges of a graph by Hamilton cycles and prove that if a graph with maximum degree ∆ satisfies some basic expansion properties and contains a family of (1−o(1))∆/2 edge disjoint Hamilton cycles, then there also exists a covering of its...

A. D. Davis, G. D. Wells, B. Falk, and M. D. Noseworthy Medical Physics and Applied Radiation Sciences, McMaster University, Hamilton, Ontario, Canada, Medical Physics and Applied Radiation Sciences, St. Joseph's Healthcare, Hamilton, Ontario, Canada, Department of Anesthesia, University of Toronto, Toronto, Ontario, Canada, Physiology and Experimental Medicine, The Hospital for Sick Children, ...

Let G(n, r, s) denote a uniformly random r-regular s-uniform hypergraph onn vertices, where s is a fixed constant and r = r(n) may grow with n. An `-overlapping Hamilton cycle is a Hamilton cycle in which successive edges overlapin precisely ` vertices, and 1-overlapping Hamilton cycles are called loose Hamiltoncycles.When r, s ≥ 3 are fixed integers, we establish a thre...

A cycle in a graph G is called a hamilton cycle if it contains every vertex of G. A l-factor of a graph G is a subgraph H of G with the same vertex set as G, such that each vertex of H has degree one. Ringel [S] has generalized the idea of a hamilton cycle to two dimensions. He showed that if n is odd the set of squares in the n-dimensional cube Q,, can be partitioned into subsets such that eac...

We show that every sufficiently large r-regular digraph G which has linear degree and is a robust outexpander has an approximate decomposition into edge-disjoint Hamilton cycles, i.e. G contains a set of r−o(r) edge-disjoint Hamilton cycles. Here G is a robust outexpander if for every set S which is not too small and not too large, the ‘robust’ outneighbourhood of S is a little larger than S. T...

Deep vein thrombosis (DVT) is a condition, in which an obstruction of blood flow in veins is found due to the formation of blood clots in the deep veins. An objective diagnosis of DVT is based on ultrasonography examination. However, in poor countries, including Indonesia, many hospitals still do not have the facilities of ultrasonography, less vascular specialists, or D-dimer examination and t...

We consider the complexity of the Hamilton cycle decision problem when restricted to k-uniform hypergraphs H of high minimum codegree δ(H). We show that for tight Hamilton cycles this problem is NP-hard even when restricted to k-uniform hypergraphsH with δ(H) ≥ n2−C, where n is the order of H and C is a constant which depends only on k. This answers a question raised by Karpiński, Ruciński and ...

The illiquid market model HJB equations and characterization of the solution Power utility functions and numerical results

In this paper we provide a maximum norm analysis of an overlapping Schwarz method on non-matching grids for evolutionary HJB equation with nonlinear source terms with the mixed boundary conditions and a general elliptic operator. Moreover, an asymptotic behavior in uniform norm is established.