The number of 8-cycles in 2-factorizations of Kn

A Quantitative Approach to Perfect One-Factorizations of Complete Bipartite Graphs

Given a one-factorization F of the complete bipartite graph Kn,n, let pf(F) denote the number of Hamiltonian cycles obtained by taking pairwise unions of perfect matchings in F . Let pf(n) be the maximum of pf(F) over all one-factorizations F of Kn,n. In this work we prove that pf(n) > n2/4, for all n > 2. 1 Perfect one-factorizations A one-factorization of a graph G is a partition of its set o...

On the Defining Number of (2n - 2)-Vertex Colorings of Kn x Kn

Double Dudeney sets for an odd number of vertices

A double Dudeney set in Kn is a multiset of Hamilton cycles in Kn having the property that each 2-path in Kn lies in exactly two of the cycles. In this paper, we construct a double Dudeney set in Kn when n = p1p2 · · · ps + 2, where p1, p2, . . . , ps are different odd prime numbers and s is a natural number.

Assessment of Changes in Shear Strength Parameters for Soils below Circular Machine Foundation

This paper focuses on the response of circular machine foundation resting on different soils (sand and clay) through studying the variation of soil shear strength parameters and strain with the number of cycles. The objective of the current study is to explore the results related to the parameters of the dynamic load (number of loading cycles and frequency of load) related to the circular footi...

Pancomponented 2-factorizations of complete graphs

We pose and solve the existence of 2-factorizations of complete graphs and complete bipartite graphs that have the number of cycles per 2-factor varying, called pancomponented. Such 2-factorizations exist for all such graphs. The pancomponented problem requires a slight generalization of the methods used to solve pancyclic 2-factorization problem, by building 2-factors from cyclically generated...