For an undirected graph and a fixed integer k, a 2-matching is said to be Ck-free if it has no cycle of length k or less. The problem of finding a maximum cardinality Ck-free 2-matching is polynomially solvable when k ≤ 3, and NP-hard when k ≥ 5. It is known that the polynomial solvability of this problem is closely related to jump systems. Indeed, the degree sequences of the Ck-free 2-matching...

In this work, the spatial resolution of two quantum well intermixing processes has been obtained using spatially resolved photoluminescence. The processes investigated are impurity-free vacancy disordering using SiO2/SiO2:P caps and sputtered silica induced intermixing. These studies aimed to choose a suitable intermixing technology to realize the band gap gratings for domain disordering quasi-...

This paper investigates two different local search approaches for the TSP. Both approaches are based on the general concept of single-alternating cycle neighborhoods. The first approach, stems from the famous heuristic suggested by Lin and Kernighan and the second is based on the notion of stemand-cycles developed by Glover in the early nineties. We show that the corresponding neighborhoods are...

In this work, we propose a high resolution Alternating Evolution Discontinuous Galerkin (AEDG) method to solve Hamilton-Jacobi equations. The construction of the AEDG method is based on an alternating evolution system of the Hamilton-Jacobi equation, following the previous work [H. Liu, M. Pollack and H. Saran, SIAM J. Sci. Comput. 35(1), (2013) 122–149] on AE schemes for Hamilton-Jacobi equati...

Open problems submitted to the 2nd Canadian Discrete and Algorithmic Mathematics Conference will be held on May 25-28, 2009, at the Centre de recherches mathématiques in Montréal, Canada. put brief summary here Comments and questions of a technical nature about a particular problem should be sent to the correspondent for that problem. Please send other comments and information about partial or ...

A decomposition of a graph is set subgraphs whose edges partition those $G$. The 3-decomposition conjecture posed by Hoffmann-Ostenhof in 2011 states that every connected cubic can be decomposed into spanning tree, 2-regular subgraph, and matching. It has been settled for special classes graphs, one the first results being Hamiltonian graphs. In past two years several new have obtained, adding ...

Orthogonal matching pursuit (OMP) is a widely used compressive sensing (CS) algorithm for recovering sparse signals in noisy linear regression models. The performance of OMP depends on its stopping criteria (SC). SC for OMP discussed in literature typically assumes knowledge of either the sparsity of the signal to be estimated k0 or noise variance σ , both of which are unavailable in many pract...

a r t i c l e i n f o a b s t r a c t In a recently published paper [Z.-J. Xue, S.-Y. Liu, An optimal result on fault-tolerant cycle-embedding in alternating group graphs, Inform. the authors showed that for a set of faulty vertices F in an n-dimensional alternating group graph AG n , AG n − F remains pancyclic if |F | 2n − 6. However, the proof of the result is flawed. We will prove the theore...