In the first part of the thesis we define an automorphism φn for each star graph Stn of degree n − 1, which yields permutations of labels for the edges of Stn taken from the set of integers {1, . . . , bn/2c}. By decomposing these permutations into permutation cycles, we are able to identify edge-disjoint Hamilton cycles that are automorphic images of a known two-labelled Hamilton cycle H1 2(n)...

This paper intends to harmonize two different approaches to the analysis of the business cycle and in doing so it retrieves the stylized facts of the business cycle in Europe. We start with the ‘classical’ approach proposed in Burns and Mitchell (1946) of dating and analyzing the business cycle; we then adopt the ‘modern’ alternative: the Markov-switching time series model proposed in Hamilton ...

A study was conducted to determine the breeding season of endangered Nandus nandus by observing fecundity, somatic indexes, and gonadal cycle development year-round. Samples were collected from different fish landing centers Sadar Upazila Gazipur district. GSI values N. ranged 4.26 ± 0.45 10.28 0.39 while maximum minimum observed in July October, respectively. However, GaSI showed an inverse re...

objective : patients with chronic physical diseases sometimes show increased loss of function; such patients need more care. anxiety is a well-known symptom that is prevalent among chronic obstructive pulmonary disease patients that can prolong and increase the risk of hospitalization. the purpose of this study was to evaluate the severity of anxiety in the mentioned patients and to examine the...

Let n = 2k + 1 with 0 < k ∈ Z and let Mk be the subgraph induced by the kand (k + 1)-levels of the n-cube graph. A system of numeration according to which the nonnegative integers are written as restricted growth strings, so called by Arndt and Ruskey, has specifically the k-th Catalan number Ck = (n k ) /n expressed as 10k. This permits a linear ordering of the vertex set of a quotient graph R...

Given a function f : N → R, call an n-vertex graph f-connected if separating off k vertices requires the deletion of at least f(k) vertices whenever k ≤ (n− f(k))/2. This is a common generalization of vertex connectivity (when f is constant) and expansion (when f is linear). We show that an f -connected graph contains a cycle of length linear in n if f is any linear function, contains a 1-facto...

In this paper, we prove that a 2-connected weighted graph G contains either a Hamilton cycle or a cycle of weight at least 2m/3 if it satisfies the following conditions: (1) ∑3 i=1 d (vi) ≥ m, where v1, v2 and v3 are three pairwise nonadjacent vertices of G, and two of them are nonadjacent vertices of an induced claw or an induced modified claw; (2) In each induced claw and each induced modifie...

An intriguing open question is whether the graph formed by the middle two levels of the Boolean lattice of subsets of a k element set has a Hamilton path for all k We consider nding a lower bound on the length of the longest cycle in this graph A result of Babai for vertex transitive graphs gives a lower bound of N where N is the total number of vertices in the middle two levels In this paper w...

The k{restricted 2{factor problem is that of nding a spanning subgraph consisting of disjoint cycles with no cycle of length less than or equal to k. It is a generalization of the well known Hamilton cycle problem and is equivalent to this problem when n 2 k n ? 1. This paper considers necessary and suucient conditions, algorithms, and polyhedral conditions for 2{factors in bipartite graphs and...

Henning and Yeo [SIAM J. Discrete Math. 26 (2012) 687–694] conjectured that a 3-regular digraph D contains two vertex disjoint directed cycles of different length if either D is of sufficiently large order or D is bipartite. In this paper, we disprove the first conjecture. Further, we give support for the second conjecture by proving that every bipartite 3-regular digraph, which either possesse...