Abs t rac t . In this note a greedy algorithm is considered that computes a matching for a graph with a given ordering of its vertices, and those graphs are studied for which a vertex ordering exists such that the greedy algorithm always yields maximum cardinality matchings for each induced subgraph. We show that these graphs, called greedy matchable graphs, are a subclass of weakly triangulate...

By using a modified argument, we prove an improvement of our former Altman type generalization of the Brézis–Browder ordering principle which yields a stronger maximum principle.

Let Γ be a graph on n vertices, adjacency matrix A, and distinct eigenvalues λ > λ1 > λ2 > · · · > λd. For every k = 0, 1, . . . , d−1, the k-alternating polynomial Pk is defined to be the polynomial of degree k and norm ‖Pk‖∞ = max1≤l≤d{|Pk(λl)|} = 1 that attains maximum value at λ. These polynomials, which may be thought of as the discrete version of the Chebychev ones, were recently used by ...

We show that the pseudoflow algorithm for maximum flow is particularly efficient for the bipartite matching problem both in theory and in practice. We develop several implementations of the pseudoflow algorithm for bipartite matching, and compare them over a wide set of benchmark instances to state-ofthe-art implementations of push-relabel and augmenting path algorithms that are specifically de...

The eeciency of a parallel implementation of the conjugate gradient method precon-ditioned by an incomplete Cholesky factorization can vary dramatically depending on the column ordering chosen. One method to minimize the number of major parallel steps is to choose an ordering based on a coloring of the symmetric graph representing the nonzero adjacency structure of the matrix. In this paper, we...

this paper submitting the computation of optimize point of ordering in inventory control systems and particularly for continuous review of ordering system (r,q) by fuzzy logic method which similarly can be used for other ordering systems. since in the ordering models we cannot forecast the parameters like cost exactly, we have ambiguity. in this case using precise parameters may cause wrong dec...

There are several sections. The goal is to link complex analysis and imbeddings of graphs so that graph imbeddings can be performed systematically using identification spaces based on group actions in the complex plane. We give a short primer of basic calculus and then explain some of the finer aspects that obfuscate a complete solution to the Riemann Hypothesis. This is not central to our main...

where B = d 4 I− A 2 and Ei is a matrix whose i th diagonal entry is 1 and the others are 0. From now on let’s assume G is d-regular (i.e. each vertex has degree exactly d). Then the adjacency matrix A has at most d non-zero entries, each equal to 1/2, in every row, so ‖A‖ ≤ d/2 and 0 B d 2 I. Note that if α is the optimal value for the SDP we have |E| 2 = nd 4 ≤ α ≤ |E| = nd 2 . The first ineq...

We investigate natural extensions of the Continuous Image Graph (CIG) labelling scheme, which is based on the Consecutive Ones Property of matrices. The CIG labelling scheme generalizes tree labelling schemes to many graphs yet remaining as efficient, i.e., adjacency tests run in constant time, the space requirement is constant per node, and testing whether a graph is a CIG is possible in polyn...