Let G = (V,E) be a multigraph (it has multiple edges, but no loops). We call G maximally edge-connected if λ(G) = δ(G), and G super edge-connected if every minimum edge-cut is a set of edges incident with some vertex. The restricted edgeconnectivity λ′(G) of G is the minimum number of edges whose removal disconnects G into non-trivial components. If λ′(G) achieves the upper bound of restricted ...

We show that for every cubic graph G with sufficiently large girth there exists a probability distribution on edge-cuts of G such that each edge is in a randomly chosen cut with probability at least 0.88672. This implies that G contains an edge-cut of size at least 1.33008n, where n is the number of vertices of G, and has fractional cut covering number at most 1.12776. The lower bound on the si...

MAX CUT is the problem of partitioning the vertices of a graph into two sets max imizing the number of edges joining these sets This problem is NP hard Goemans and Williamson proposed an algorithm that rst uses a semide nite programming relaxation of MAX CUT to embed the vertices of the graph on the surface of an n dimensional sphere and then uses a random hyperplane to cut the sphere in two gi...

Let C = (V, E) be an undirected graph, w : E + Z’ a weight function and T c V an even subset of vertices from G. A T-cut is an edge-cut set which divides T into two odd sets. For ( Tj = 4 Seymour gave a good characterization of the graphs for which there exists a maximum packing of T-cuts that is integral. Based on Seymour’s characterization we provide a simple 0(n3m + PI”&) algorithm for incre...

The strong product G1 £G2 of graphs G1 and G2 is the graph with V (G1) × V (G2) as the vertex set, and two distinct vertices (x1, x2) and (y1, y2) are adjacent whenever for each i ∈ {1, 2} either xi = yi or xiyi ∈ E(Gi). In this note we show that for two connected graphs G1 and G2 the edge-connectivity λ(G1£G2) equals min{δ(G1£ G2), λ(G1)(|V (G2)|+2|E(G2)|), λ(G2)(|V (G1)|+2|E(G1)|)}. In additi...

Given an edge-capacitated undirected graph G = (V ,E,C) with edge capacity c :E → R+, n = |V |, an s − t edge cut C of G is a minimal subset of edges whose removal from G will separate s from t in the resulting graph, and the capacity sum of the edges in C is the cut value of C. A minimum s − t edge cut is an s − t edge cut with the minimum cut value among all s − t edge cuts. A theorem given b...

Since shot boundaries with less than five frames are classified as “cuts” in the TRECVID evaluation, the results for SG are added to the results in CUT, and are submitted as the results for “cuts”. For the cut detection, we use two linear kernel SVMs (one for CUT and the other for SG) with different feature sets. The features for a CUT-SVM are activity ratio (the ratio of “dynamic” pixels to al...

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...

An edge cut that separates the connected graph into components with order at least two is restricted edge cut. The cardinality of minimum restricted edge cut is restricted edge connectivity. Denote byλ′ ( G) the restricted edge connectivity , then λ′( G) ≤ξ( G) where ξ( G) is the minimum edge degree. G is called maximal restricted edge connected if the equality in the previous inequality holds....