An arc in a tournament T with n ≥ 3 vertices is called pancyclic if it belongs to a cycle of length l for all 3 ≤ l ≤ n. We call a vertex u of T an out-arc pancyclic vertex of T if each out-arc of u is pancyclic in T . Yao, Guo and Zhang [Discrete Appl. Math. 99 (2000), 245–249] proved that every strong tournament contains at least one out-arc pancyclic vertex, and they gave an infinite class o...

We investigate the parameterized complexity of Vertex Cover parameterized above the optimum value of the linear programming (LP) relaxation of the integer linear programming formulation of the problem. By carefully analyzing the change in the LP value in the branching steps, we argue that even the most straightforward branching algorithm (after some preprocessing) results in an O∗(2.6181r) algo...

We develop a theory of removable singularities for the weighted Bergman space Aμ(Ω) = {f analytic in Ω : R Ω |f | dμ < ∞}, where μ is a Radon measure on C. The set A is weakly removable for Aμ(Ω \ A) if Aμ(Ω \ A) ⊂ Hol(Ω), and strongly removable for Aμ(Ω \A) if Aμ(Ω \A) = Aμ(Ω). The general theory developed is in many ways similar to the theory of removable singularities for Hardy H spaces, BMO...

A vertex|matching-partition (V |M) of a simple graph G is a spanning collection of vertices and independent edges of G. Let vertex v ∈ V have weight wv and edge e ∈ M have weight we. Then the weight of V |M is w(V |M) = ∏ v∈V wv · ∏ e∈M we. Define the vertex|matching-partition function of G as W(G) = ∑ V |M w(V |M). In this paper we study this function when G is a path and a cycle. We generate ...

Although the benefits of implant-borne removable prostheses are readily apparent for the fully edentulous patient and have been well documented, there is a paucity of studies concerning the combination of implants with removable partial dentures in partially edentulous patients. The aim of this article is to review the literature regarding implants with removable partial dentures and evaluate t...

I.Cahit introduced cordial graphs as a weaker version of graceful and harmonious graphs. The total product cordial labeling is a variant of cordial labeling. In this paper we introduce a vertex analogue product cordial labeling as a variant of total product cordial labeling and name it as total vertex product cordial labeling. Finally, we investigate total vertex product cordial labeling for ma...

A classic result of G. A. Dirac in graph theory asserts that every n-vertex graph (n ≥ 3) with minimum degree at least n/2 contains a spanning (so-called Hamilton) cycle. G. Y. Katona and H. A. Kierstead suggested a possible extension of this result for k-uniform hypergraphs. There a Hamilton cycle of an n-vertex hypergraph corresponds to an ordering of the vertices such that every k consecutiv...

For the Odd Cycle Transversal problem, task is to find a small set S of vertices in graph that intersects every cycle odd length. The Subset requires intersect only those cycles include vertex distinguished subset T. If we are given weights for vertices, ask instead has weight: this problem Weighted Transversal. We prove an almost-complete complexity dichotomy graphs do not contain H as induced...

For a graph G, let γ(G) denote the domination number of G and let δ(G) denote the minimum degree among the vertices of G. A vertex x is called a bad-cut-vertex of G if G−x contains a component, Cx, which is an induced 4-cycle and x is adjacent to at least one but at most three vertices on Cx. A cycle C is called a special-cycle if C is a 5-cycle in G such that if u and v are consecutive vertice...

OBJECTIVES To evaluate the effect of age and chosen factors related to aging such as dentition, muscle strength, and nutrition on masticatory muscles electromyographic activity during chewing in healthy elderly women. BACKGROUND With longer lifespan there is a need for maintaining optimal quality of life and health in older age. Skeletal muscle strength deteriorates in older age. This deterio...