A randomized (Las Vegas) algorithm is given for nding the Gallai-Edmonds decomposition of a graph. Let n denote the number of vertices, and let M(n) denote the number of arithmetic operations for multiplying two n n matrices. The sequential running time (i.e., number of bit operations) is within a poly-logarithmic factor of M(n). The parallel complexity is O((log n) 2) parallel time using a num...

A randomized (Las Vegas) algorithm is given for finding the Gallai–Edmonds decomposition of a graph. Let n denote the number of vertices, and let M(n) denote the number of arithmetic operations for multiplying two n×n matrices. The sequential running time (i.e., number of bit operations) is within a poly-logarithmic factor of M(n). The parallel complexity is O((logn)2) parallel time using a num...

This paper documents efforts to develop an instrument to measure mathematical knowledge for teaching high school geometry (MKT-G). We report on the process of developing and piloting questions that purported to measure various domains of MKT-G. Scores on the final set of items had no statistical relationship with total years of experience teaching, but all domain scores were found to have stati...

We prove the following Gallai-type equality

In the present paper we extend following three coloring concepts for class of finite undirected graphs having multiple edges but no loops. First all, generalized concept, in which same colored vertices a graph induce subgraph satisfying prescribed property. Secondly, concept variable degeneracy, was introduced by Borodin, Kostochka and Toft 2000; this makes it possible to give common generaliza...

A randomized (Las Vegas) algorithm is given for nding the Gallai-Edmonds decomposition of a graph. Let n denote the number of vertices, and let M(n) denote the number of arithmetic operations for multiplying two n n matrices. The sequential running time (i.e., number of bit operations) is within a poly-logarithmic factor of M(n). The parallel complexity is O((log n) 2) parallel time using a num...

Abstract: For many years, the bulk of research on mathematics teacher learning has consisted of small-scale qualitative studies. While this work has made significant advances in identifying and explicating instructional practices that have the potential for affording all students equitable access to high-quality classroom learning opportunities, what teacher learning and improvement looks like ...

The Absolute Measurement Session during the XIVth IAGA Workshop on Geomagnetic Observatory Instruments, Data Acquisition and Processing was held at the Changchun Magnetic Observatory (CNH) September 14-17, 2010. Approximately 50 participants joined in this session. During the session, 27 DI-Flux magnetometers were used to make and compare measurements, and several total field comparison measure...