A cycle cover of a directed graph is a collection of node disjoint cycles such that every node is part of exactly one cycle. A k-cycle cover is a cycle cover in which every cycle has length at least k. While deciding whether a directed graph has a 2-cycle cover is solvable in polynomial time, deciding whether it has a 3-cycle cover is already NP-complete. Given a directed graph with nonnegative...

In this paper we study the problem of finding the minimum cycle mean in the weighted directed graph. The computational aspect of some algorithms for solving this problem is discussed and two algorithms for minimum cycle mean finding in the weighted directed graph are proposed.

Objective(s):Multidrug resistance (MDR) of cancer cells is a major obstacle to successful chemotherapy. Overexpression of breast cancer resistance protein (BCRP) is one of the major causes of MDR. In addition, it has been shown that PI3K/Akt signaling pathway involves in drug resistance. Therefore, we evaluated the effects of novel approaches including siRNA directed against BCRP and targeted t...

Let D be a directed graph of order n. An anti-directed (hamiltonian) cycleH inD is a (hamiltonian) cycle in the graph underlyingD such that no pair of consecutive arcs in H form a directed path in D. In this paper we give sufficient conditions for the existence of anti-directed hamiltonian cycles. Specifically, we prove that a directed graph D of even order n with minimum indegree and outdegree...

To describe the dynamics of stage-structured populations with m stages living in n patches, we consider matrix models of the form SD, where S is a block diagonal matrix with n× n column substochastic matrices S1, . . . , Sm along the diagonal and D is a block matrix whose blocks aren× n nonnegative diagonal matrices. The matrix S describes movement between patches and the matrix D describes gro...

A directed k-cycle system of order n is a pair ( S, T ), where S is an n-set and T is a collection of arc disjoint directed k-cycles that partition the complete directed graph Kn *. An almost parallel class with deficiency x is a set of directed k-cycles which form a partition of S \ {x}. An almost resolvable directed k-cyclc system is a directed k-cyclc system in which the cycles can be partit...

It was conjectured by Caccetta and Häggkvist in 1978 that every digraph G with n vertices and minimum outdegree at least r contains a directed cycle of length at most dn=re. By refining an argument of Chvátal and Szemerédi, we prove that such G contains a directed cycle of length at most n=r þ 73.

Analysis with the Weibull distribution method shows that right treatment recommendations for treating air cycle machine (ACM) in form of category preventive maintenancetime directed (TD), due to maintenanceTime Directed (TD) is a maintenance can be carried out if time variable component or system known and directly aims prevent damage.

We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph G whose edges have non-negative weights. A cycle in this graph is actually a cycle in the underlying undirected graph with edges traversable in both directions. A {−1,0,1} edge incidence vector is associated with each cycle: edges traversed by the cycle in the right dire...

We consider the problem of computing a minimum cycle basis in a directed graph. The input to this problem is a directed graph G whose edges have non-negative weights. A cycle in this graph is actually a cycle in the underlying undirected graph with edges traversable in both directions. A f 1;0;1g edge incidence vector is associated with each cycle: edges traversed by the cycle in the right dire...