~'Ve presenl efficienl. algorithms faT' cllO'I'dal bipartite graphs. Both algorit.hms 'lise a doubly /c.1;icaf ordering of the bipaTii-fe adjacency 'IIIa-tri.r. The first algol'dhm. computes a perfect edge with.out I;ert.c): elimination ordering (l.nd 1-he second one tisls all ma:l:im,al c01l1plete bipartite sttbgrap/Js. Keywol'ds: Dcsiqll of algorithms. effieiellt a.lgorithms. chordal biJlorti...

The adjacency matrix is the most fundamental and intuitive object in graph analysis that useful not only mathematically but also for visualizing structures of graphs. Because appearance an critically affected by ordering rows columns, or vertex ordering, statistical assessment graphs together with their sequences important identifying characteristic In this paper, we propose a hypothesis testin...

Given positive integers m,n, s, t, let z (m,n, s, t) be the maximum number of ones in a (0, 1) matrix of size m× n that does not contain an all ones submatrix of size s× t. We show that if s ≥ 2 and t ≥ 2, then for every k = 0, . . . , s− 2, z (m,n, s, t) ≤ (s− k − 1) nm + kn+ (t− 1)m. This generic bound implies the known bounds of Kövari, Sós and Turán, and of Füredi. As a consequence, we also...

We propose an inexact method for the graph Fourier transform of a graph signal, as defined by the signal decomposition over the Jordan subspaces of the graph adjacency matrix. This method projects the signal over the generalized eigenspaces of the adjacency matrix, which accelerates the transform computation over large, sparse, and directed adjacency matrices. The trade-off between execution ti...

We survey and present new geometric and combinatorial properties of some polyhedra with application in combinatorial optimization, for example, the max-cut and multicommodity ow problems. Namely we consider the volume, symmetry group, facets, vertices, face lattice, diameter, adjacency and incidence relations and connectivity of the metric polytope and its relatives. In particular, using its la...

Abst rac t . We survey and present new geometric and combinatorial propertiez of some polyhedra with application in combinatorial optimization, for example, the max-cut and multicommodity flow problems. Namely we consider the volume, symmetry group, facets, vertices, face lattice, diameter, adjacency and incidence relm :ons and connectivity of the metric polytope and its relatives. In partic~da...