We show that the Min Cut Linear Arrangement Problem (Min Cut) is NP-complete for trees with polynomial size edge weights and derive from this the NP-completeness of Min Cut for planar graphs with maximum vertex degree 3. This is used to show the NP-completeness of Search Number, Vertex Separation, Progressive Black/ White Pebble Demand, and Topological Bandwidth for planar graphs with maximum v...

PURPOSE To introduce and determine the biopsy length performance of the novel enhanced cutting edge (ECE) needle tip design, which contains high inclination angles that allow for more efficient tissue cutting. METHODS ECE and regular two-plane symmetric needle tip's biopsy performance and cutting force are compared over a series of needle insertion experiments into bovine liver under varying ...

For a graph G, let     max : is an edge cut of b G D D G  . For graphs G and H, a map     :V G V H   is a graph homomorphism if for each   e uv E G   ,       u v E H    . In 1979, Erdös proved by probabilistic methods that for p ≥ 2 with

Aluminium additions to metallic coatings on steel substrates have been accepted as a successful solution versus the standard zinc based coatings. The development of these products responds to the market’s demand of more versatile products, which faces the leaching effect of zinc and the rising cost of obtaining this element, among the main advantages. However, these materials show a special sen...

1.1. Preamble. Given a graph G = V E and a subset A ⊆ V , the cut determined by A is the vector A ∈ ±1 E with ijth entry −1 if and only if A∩ i j = 1. The cut polytope CUT G is the polytope in E defined as the convex hull of all cuts A (A⊆ V ). Given edge weights w ∈ E , the max-cut problem is the problem of finding a cut A whose weight ∑ ij∈E i∈A j ∈A wij is maximum. Hence, it can be formulate...

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This paper presents insertions-only algorithms for maintaining the exact and/or approximate size of the minimum edge cut and the minimum vertex cut of a graph. The algorithms output the approximate or exact size k in time O(1) and a cut of size k in time linear in its size. For the minimum edge cut problem and for any 0 < 1, the amortized time per insertion is O(1== 2) for a (2 +)-approximation...

PURPOSE To determine the cutting characteristics of seven different microkeratomes and to compare the cut edges and surface characteristics of the corneas with respect to different keratome parameters, ie, blade oscillation frequencies and keratome speed. METHODS Lamellar keratectomies were performed using each microkeratome on eight freshly enucleated porcine corneas. The freshly cut corneal...

The cut polyhedron cut(G) of an undirected graph G = (V,E) is the dominant of the convex hull of all its nonempty edge cutsets. After examining various compact extended formulations for cut(G), we study some of its polyhedral properties. In particular, we characterize all the facets induced by inequalities with right-hand side at most 2. These include all the rank facets of the polyhedron.

This study has investigated the solubility of inhibiting pigments and also the leaching behaviour of corrosion inhibitors from a polyester binder in an acid rain solution. This study has relevance to the control of cut-edge corrosion by inhibitor pigments, which are incorporated into the primer coatings of coil-coated architectural cladding. The concentrations of leachate solutions in tubes glu...