It was conjectured by Hoffmann-Ostenhof that the edge set of every connected cubic graph can be decomposed into a spanning tree, a matching and a family of cycles. In this paper, we show that this conjecture holds for traceable cubic graphs. keywords: Cubic graph, Hoffmann-Ostenhof’s Conjecture, Traceable AMS Subject Classification: 05C45, 05C70

A graph is cubic if each of its vertex is of degree 3 and it is hamiltonian if it contains a cycle passing through all its vertices. It is known that if a cubic graph is hamiltonian, then it has at least three Hamilton cycles. This paper is about those works done concerning the number of Hamilton cycles in cubic graphs and related problems.

We present a convention (for square/cubic root) which provides correct interpretations of Lagrange’s formula for all cubic polynomial equations with real coefficients. Using this convention, we also present a real solution formulas for the general cubic equation with real coefficients under equality and inequality constraints.

This paper describes a method for computing the fundamental unit and regulator of a purely cubic congruence function field of unit rank 1. The technique is based on Voronoi’s algorithm for generating a chain of successive minima in a multiplicative cubic lattice which is used for calculating the fundamental unit and regulator of a purely cubic number field.

Computing the intersection curve of two quadrics is a fundamental problem in computer graphics and solid modeling. We present an algebraic method for classifying and parameterizing the intersection curve of two quadric surfaces. The method is based on the observation that the intersection curve of two quadrics is birationally related to a plane cubic curve. In the method this plane cubic curve ...

In this paper, we investigate finite difference schemes for the 3-D wave equation using 27-point stencils on the cubic lattice, a 13-point stencil on the face-centered cubic (FCC) lattice, and a 9-point stencil on the body-centered cubic (BCC) lattice. The tiling of the wavenumber space for nonCartesian grids is considered in order to analyse numerical dispersion. Schemes are compared for compu...

We prove that every simple 2-connected cubic n-vertex graph contains a spanning closed walk of length at most 9n/7 − 1, and that such a walk can be found in polynomial time. This yields a polynomial-time 9/7-approximation algorithm for the graphic TSP for 2-connected cubic graphs, which improves the previously known approximation factor of 1.3 for 2-connected cubic graphs. On the negative side,...

The electrocatalytic properties for electro-oxidation reactions of shape-controlled Pt-based catalysts have been improved by alloying with 2nd elements. In this study, we demonstrate cubic PtPd alloy nanoparticles synthesized using a thermal decomposition method. The cubic PtPd nanoparticles exhibit a homogeneous distribution of alloy nanostructures in the presence of Pt and Pd metallic phases....

Multiphase (MP) monoclinic and cubic Y2O3 nanoparticles, 40 nm in diameter, were densified by spark plasma sintering for 5–15 min and100 MPa at 1000 C, 1100 C, and 1500 C. Densification started with pressure increase at room temperature. Densification stagnated during heating compared to the high shrinkage rate in cubic single-phase reference nanopowder. The limited densification of the MP nano...

The unbalanced oil and vinegar signature scheme (UOV) is one of signature schemes whose public key is a set of multivariate quadratic forms. Recently, a new variant of UOV called Cubic UOV was proposed at Inscrypt 2015. It was claimed that the cubic UOV was more efficient than the original UOV and its security was enough. However, an equivalent secret key of the cubic UOV can be recovered easil...