We resolve the longstanding open problem concerning computational complexity of MaxCut on interval graphs by showing that it is NP-complete.

A biclique in a graph Γ is a complete bipartite subgraph of Γ. We give bounds for the maximum number of edges in a biclique in terms of the eigenvalues of matrix representations of Γ. These bounds show a strong similarity with Lovász’s bound θ(Γ) for the Shannon capacity of Γ. Motivated by this similarity we investigate bicliques and the bounds in certain product graphs.

The knowledge of the spectrum of a (di)graph is relevant for estimating some of its structural properties, which provide information on the topological and communication properties of the corresponding networks. Among these properties, we have, for instance, edge-expansion and node-expansion, bisection width, diameter, maximum cut, connectivity, and partitions. In this paper, we determine the c...

ALK98 0.52 Figure 1 BEA98SA 0.38 Figure 2 BEA98TS 0.74 Figure 3 BUR02 0.58 Figure 4 DUA05 0.54 Figure 5 FES02G 0.78 Figure 6 FES02GP 0.76 Figure 7 FES02GV 0.58 Figure 8 FES02GVP 0.68 Figure 9 FES02V 0.30 Figure 10 FES02VP 0.22 Figure 11 GLO10 0.49 Figure 12 GLO98 0.54 Figure 13 HAS00GA 0.52 Figure 14 HAS00TS 0.49 Figure 15 KAT00 0.38 Figure 16 KAT01 0.37 Figure 17 LAG09CE 0.19 Figure 18 LAG09HC...

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...

We introduce a new class of inequalities valid for the cut polytope, which we call gap inequalities. Each gap inequality is given by a nite sequence of integers, whose \gap" is deened as the smallest discrepancy arising when decomposing the sequence into two parts as equal as possible. Gap inequalities include the hypermetric inequalities and the negative type inequalities, which have been exte...

Today we continue our discussion of exact recovery under perturbation-stability assumptions. We’ll look at a different cut problem than last lecture, and this will also give us an excuse to touch on two cool and fundamental topics, metric embeddings and semidefinite programming. The Maximum Cut problem is a famous NP -hard problem. The input is an undirected graph G = (V,E), where each edge e ∈...