In this study, turning operation of Monel K500 copper-nickel super-alloy was evaluated. Ceramic cutting tools with two different cutting noses (conventional and wiper) were utilized. At first, the experimental tests were designed by using central composite design method. After implementation of the tests, the statistical models for output data (surface roughness, cutting force, and flank wear) ...

Three methods are investigated to remove the concavity at the boundary edges and/or vertices during polyhedral mesh generation by a dual mesh method. The non-manifold elements insertion method is the first method examined. Concavity can be removed by inserting non-manifold surfaces along the concave edges and using them as an internal boundary before applying Delaunay mesh generation. Conical c...

We present a deterministic incremental algorithm for exactly maintaining the size of a minimum cut with Õ(1) amortized time per edge insertion and O(1) query time. This result partially answers an open question posed by Thorup [Combinatorica 2007]. It also stays in sharp contrast to a polynomial conditional lower-bound for the fully-dynamic weighted minimum cut problem. Our algorithm is obtaine...

We address the following problem: given an undirected graph G = (V,E), with vertex set V of cardinality n and edge set E, where each edge (i, j) has a non-negative integer weight wij , and given a constant B, 0 ≤ B < n, find a cut (S, V \ S) of G of maximum weight such that the difference between the cardinalities of the two shores of the cut is not greater than B. This problem has been introdu...

The Small Set Expansion Hypothesis is a conjecture which roughly states that it is NP-hard to distinguish between a graph with a small subset of vertices whose (edge) expansion is almost zero and one in which all small subsets of vertices have expansion almost one. In this work, we prove conditional inapproximability results with essentially optimal ratios for the following graph problems based...

Given a graph G = (V,E), let P be a partition of V . We say that P is dominating if, for each part P of P, the set V \ P is a dominating set in G (equivalently, if every vertex has a neighbour of a different colour from its own). We say that P is acyclic if for any parts P, P ′ of P, the bipartite subgraph G[P, P ′] consisting of the edges between P and P ′ in P contains no cycles. The acyclic ...

Mycielski introduced a new graph transformation μ(G) for graph G, which is called the Mycielskian of G. A graph G is super connected or simply super-κ (resp. super edge connected or super-λ), if every minimum vertex cut (resp. minimum edge cut) isolates a vertex of G. In this paper, we show that for a connected graph G with |V (G)| ≥ 2, μ(G) is super-κ if and only if δ(G) < 2κ(G), and μ(G) is s...

Abst rac t . We survey and present new geometric and combinatorial propertiez of some polyhedra with application in combinatorial optimization, for example, the max-cut and multicommodity flow problems. Namely we consider the volume, symmetry group, facets, vertices, face lattice, diameter, adjacency and incidence relm :ons and connectivity of the metric polytope and its relatives. In partic~da...

Part of this paper summarizes some of the recent developments in the study of hamiltonian line graphs and the related hamiltonian claw-free graphs. The last section of this paper solves some problems on the hamiltonian like indices from a paper by Clark and Wormald in 1983. 1. Definitions and Terminology Graphs considered here are finite and loopless. Unless otherwise noted, we follow [2] for n...

In this paper we summarize recent results on finding tight semidefinite programming relaxations for the Max-Cut problem and hence tight upper bounds on its optimal value. Our results hold for every instance of Max-Cut and in particular we make no assumptions on the edge weights. We present two strengthenings of the well-known semidefinite programming relaxation of Max-Cut studied by Goemans and...