Noteworthy results have been obtained in the turning and drilling of hardened high-strength steels using tungsten carbide based cutting tools. In a finish turning process, it was seen that surface roughness and tool flank wear followed very different trends against cutting time. The suggested explanation for this behaviour is that the profile cut into the workpiece surface is determined by the ...

We prove that every connected graph G of order n has a spanning tree T such that for every edge e of T the edge-cut defined in G by the vertex sets of the two components of T − e contains at most n 32 many edges which solves a problem posed by Ostrovskii (Minimal congestion trees, Discrete Math. 285 (2004), 219-226.)

Convexity is a notion that has been defined for subsets of R and for subsets of general graphs. A convex cut of a graph G = (V,E) is a 2-partition V1∪̇V2 = V such that both V1 and V2 are convex, i. e., shortest paths between vertices in Vi never leave Vi, i ∈ {1, 2}. Finding convex cuts is NP-hard for general graphs. To characterize convex cuts, we employ the Djoković relation, a reflexive and s...

Recently developed Ti-alloyed martensitic steels are believed to exhibit higher wear resistance than traditionally quenched and tempered medium carbon steels. However, their properties may deteriorate during thermal cutting welding as a result of microstructure tempering. This would present significant challenges for the metal fabrication industries. A decrease in strength associated with tempe...

An edge cut C of a graph G is tight if |C∩M|=1 for every perfect matching M G. Barrier cuts and 2-separation are called ELP-cuts, which two important types in covered graphs. Edmonds, Lovász Pulleyblank proved that has nontrivial cut, then it also ELP-cut. Carvalho, Lucchesi, Murty made stronger conjecture: given any G, there exists ELP-cut D does not cross C. We confirm the conjecture this pap...

For an edge-colored graph G, we call edge-cut M of G monochromatic if the edges are colored with same color. The is called disconnected any two distinct vertices separated by a edge-cut. connected disconnection number (or MD-number for short) denoted md(G), maximum colors that allowed in order to make disconnected. graphs diameter one, they complete and so their MD-numbers 1. at least 3, can co...

Now that you’re finishing CS261, you’re well equipped to comprehend a lot of advanced material on algorithms. This lecture illustrates this point by teaching you about a cool and famous approximation algorithm. In the maximum cut problem, the input is an undirected graph G = (V,E) with a nonnegative weight we ≥ 0 for each edge e ∈ E. The goal is to compute a cut — a partition of the vertex set ...