Luca Trevisan [1] presented an approximation algorithm for Max Cut based on spectral partitioning techniques. He proved that the algorithm has an approximation ratio of at least 0.531. We improve this bound up to 0.6142. We also define and extend this result for the more general Maximum Colored Cut problem.

Let e(G) denote the number of edges in a graph G, and let Ck denote a k-cycle. It is well-known that every graph has a bipartite subgraph with at least half as many edges. Győri showed that any bipartite, C6-free graph contains a C4-free subgraph containing at least half as many edges. Applying these two results in sequence we see that every C6-free graph, G, has a bipartite C4-free subgraph, H...

There are several topological results ensuring in any properly colored graph the existence of a colorful complete bipartite subgraph, whose order is bounded from below by some topological invariants of some topological spaces associated to the graph. Meunier [Electron. J. Combin., 2014] presented the first colorful type result for uniform hypergraphs. In this paper, we give some new generalizat...

Background & Objectives: Cervical cancer is the second most frequent in India, with an estimated yearly diagnosis of 1, 23,907 women and 77,348 fatalities. The prevalence cervical remains high poorer nations owing to budget constraints a lack access healthcare. By evaluating lesions colposcopically, this study sought determine validity Swede score.
 Methods: cross-sectional analytical ...

Regorafenib is an oral multi-kinase inhibitor used as salvage therapy for metastatic colorectal cancer (mCRC). We tested whether serum cytokine levels are associated with clinical outcome in the mCRC patients receiving regorafenib. Serum samples were collected before treatment start, day 21, and progressive disease, and eleven angiogenic and inflammatory cytokine serum levels were examined. Fif...

The maximum cut problem this paper deals with can be formulated as follows. Given an undirected simple graph G = (V,E) where V and E stand for the node and edge sets respectively, and given weights assigned to the edges: (wij)ij∈E , a cut δ(S), with S ⊆ V is de ned as the set of edges in E with exactly one endnode in S, i.e. δ(S) = {ij ∈ E | |S ∩ {i, j}| = 1}. The weight w(S) of the cut δ(S) is...

A biclique of a graph G is a maximal induced complete bipartite subgraph of G. The biclique graph of G denoted by KB(G), is the intersection graph of all the bicliques of G. The biclique graph can be thought as an operator between the class of all graphs. The iterated biclique graph of G denoted by KBk(G), is the graph obtained by applying the biclique operator k successive times to G. The asso...

Edwards showed that every graph of size m ≥ 1 has a bipartite subgraph of size at least m/2 + √ m/8 + 1/64− 1/8. We show that every graph of size m ≥ 1 has a bipartition in which the Edwards bound holds, and in addition each vertex class contains at most m/4 + √ m/32 + 1/256 − 1/16 edges. This is exact for complete graphs of odd order, which we show are the only extremal graphs without isolated...