It is proven that for any integer $g \ge 0$ and $k \in \{ 0, \ldots, 10 \}$, there exist infinitely many 5-regular graphs of genus $g$ containing a 1-factorisation with exactly $k$ pairs 1-factors are perfect, i.e. form hamiltonian cycle. For = 0$, this settles problem Kotzig from 1964. Motivated by Labelle's "marriage" operation, we discuss two gluing techniques aimed at producing high cyclic ...

In this paper we give optimal optimal vertex degree conditions that guarantee connection by short paths in ε-regular bipartite graphs. We also study a related question of decomposing an arbitrary graph into subgraphs of small diameter.

Let Γ denote a Q-polynomial distance-regular graph with diameter D ≥ 3 and standard module V . Recently Ito and Terwilliger introduced four direct sum decompositions of V ; we call these the (μ, ν)–split decompositions of V , where μ, ν ∈ {↓, ↑}. In this paper we show that the (↓, ↓)–split decomposition and the (↑, ↑)–split decomposition are dual with respect to the standard Hermitian form on V...

In this paper, we study the Bauer-Fike type theorems for regular matrix pairs and its general form. Besides these, we also obtain some bounds for measuring approximate generalized eigenvalues and for the perturbation of generalized eigenvalues concerning an approximate generalized invariant subspace. To estimate all these bounds, p-Hölder norm and an ad hoc pseudo-metric called p-Chordal matric...

Homomorphism duality pairs play a crucial role in the theory of relational structures and in the Constraint Satisfaction Problem. The case where both classes are finite is fully characterized. The case when both side are infinite seems to be very complex. It is also known that no finite-infinite duality pair is possible if we make the additional restriction that both classes are antichains. In ...

We introduce the Theory and Methods Special Issue on Precision Medicine Individualized Policy Discovery. The issue consists of four discussion papers, grouped into two pairs, sixteen regular research papers that cover many important lines data-driven decision making. hope provocative original ideas presented herein will inspire further work development in precision medicine personalization.

Triangular sets appear under various names in many papers concerning systems of polynomial equations. Ritt (1932) introduced them as characteristic sets. He described also an algorithm for solving polynomial systems by computing characteristic sets of prime ideals and factorizing in field extensions. Characteristic sets of prime ideals have good properties but factorization in algebraic extensi...

We study the convergence of an iterative projection/reflection algorithm originally proposed for solving what are known as phase retrieval problems in optics. There are two features that frustrate any analysis of iterative methods for solving the phase retrieval problem: nonconvexity and infeasibility. The algorithm that we developed, called Relaxed Averaged Alternating Reflections (RAAR), was ...

Abstract The endings of Spanish nouns reflect gender with varying degrees frequency and regularity. most common regular are -o for masculine -a feminine nouns, - o being more frequent less closely associated a specific category (masculine) than . Pairs words occurring both categories differ in the frequencies which they used as or forms: médic-o/médic-a ‘doctor’ (m.)/‘doctor’ (f.) is clear exam...

This paper presents a statistically based method for spotting target words in documents. The crux of the method is the representation of a word by a spatial (pla-nar) point process evolving on a regular lattice of coordinate pairs. This is accomplished by extracting the coordinate pairs, i.e. pixel locations, where the binary bitmap values of the word are non-zero. With this representation the ...