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 ...

A graph X is max-λ if λ(X) = δ(X). A graph X is super-λ if X is max-λ and every minimum edge-cut set of X isolates one vertex. In this paper, we proved that for all but a few exceptions, the mixed Cayley graph which is defined as a new kind of semi-regular graph is max-λ and super-λ. c © 2008 Elsevier B.V. All rights reserved.

We obtain three results concerning the topological cycle space C of a locally finite connected graph G. Confirming a conjecture of Diestel we show that through every edge set E ∈ C there is a topological Euler tour, a continuous map from the circle S to the end compactification |G| of G that traverses every edge in E exactly once and traverses no other edge. Second, we show that for every seque...

In this paper, by means of fuzzy approaches, an accurate method is introduced for edging of color photographs. The difference between our method with other similar methods is the use of a morphological operation to think or thick the obtained edges. In this proposed method, a 3×3 window is dragged on the photo. For each block, 12 point sets will be defined, each including two non-overlapping po...

A 4-restricted edge cut is an edge cut of a connected graph which disconnects the graph, where each component has order at least 4. Graphs that contain 4-restricted edge cuts are characterized in this paper. As a result, it is proved that a connected graph G of order at least 10 contains 4-restricted edge cuts if and only if it contains no cut-vertex u where every component of G \ u has order a...