Baker [1] devised a powerful technique to obtain approximation schemes for various problems restricted to planar graphs. Her technique can be directly extended to various other graph classes, among the most general ones the graphs avoiding a fixed apex graph as a minor. Further generalizations (e.g., to all proper minor closed graph classes) are known, but they use a combination of techniques a...

A graph G is an apex graph if it contains a vertex w such that G − w is a planar graph. It is easy to see that the genus g(G) of the apex graph G is bounded above by τ − 1, where τ is the minimum face cover of the neighbors of w, taken over all planar embeddings of G−w. The main result of this paper is the linear lower bound g(G) ≥ τ/160 (if G − w is 3-connected and τ > 1). It is also proved th...

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A graph G is an apex graph if it contains a vertex w such that G w is a planar graph It is easy to see that the genus g G of the apex graph G is bounded above by where is the minimum face cover of the neighbors of w taken over all planar embeddings of G w The main result of this paper is the linear lower bound g G if G w is connected and It is also proved that computing the genus of apex graphs...

Background and Aim: Preparation of root canal with rotary nickel-titanium (NiTi) instruments may potentially create microcracks that can lead to vertical root fracture. This study aimed to compare the incidence of crack formation by BioRaCe and Edge Taper Platinum systems in the mesiobuccal canals of extracted first mandibular molars. Materials and Methods: In this experimental study, 50 first...

The clique cover width of G, denoted by ccw(G), is the minimum value of the bandwidth of all graphs that are obtained by contracting the cliques in a clique cover of G into a single vertex. For i = 1, 2, ..., d, let Gi be a graph with V (Gi) = V , and let G be a graph with V (G) = V and E(G) = ∩di=1(Gi), then we write G = ∩di=1Gi and call each Gi, i = 1, 2, ..., d a factor of G. The case where ...

This paper investigates response of triangular shell strip footings situated on the sandy slope. A series of reduced-scale plate load tests were conducted to cover different parameters including three shell footing types with different apex angles in addition to a flat footing, four different distances for strip footings from the crest of the slope namely “edge distance” and reinforcement statu...

Background: Gestational diabetes mellitus affects 3-5% of all human pregnancy.Studies reported the neurotoxic effect of gestational diabetes on cerebellarand spinal cord in rat offspring. This study was conducted to determine the effect of gestational diabetes on astrocyte density in the cerebellum of rat offspring. Materials and Methods: In this experimental study, 30 Wistar rats dams were ran...

introduction: the purpose of this in vitro study was to compare the accuracy of the new electronic apex locator raypex5 with radiography for working length determination of straight and curved root canals. materials and methods: twenty straight and single canals of maxillary central teeth and twenty curved mesiobuccal canals of mandibular molar teeth were used. access cavities were prepared and...

Proteome scale absolute quantification is fundamental for the quantitative understanding of an organism. The unsatisfactory accuracy for protein abundance estimation of current algorithms has been partially improved by the Absolute Protein EXpression profiling (APEX) algorithm, which implements the prior expectations of peptides' appearances in the calculation of protein abundances. However, th...