Weighted Well-Covered Claw-Free Graphs

A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space. Given an input claw-free graph G, we present an O(n^6)algortihm, whose input is a claw-free graph G, and output is the vector space of weight functions w, for which G is w-well-covered. A graph G is equimatchable if all its maximal matchings are of the same cardinality. Assume that a weight function w is defined on the edges of G. Then G is w-equimatchable if all its maximal matchings are of the same weight. For every graph G, the set of weight functions w such that G is w-equimatchable is a vector space. We present an O(m*n^4 + n^5*log(n)) algorithm which receives an input graph G, and outputs the vector space of weight functions w such that G is w-equimatchable.Comment: 14 pages, 1 figur

Learning to swim as an adult

While an abundance of information is readily available for teaching the infant/child to swim, there is a lack of information available for teaching the adult who does not swim. Thus the purpose of this manual is to develop an instructional tool that will benefit the adult learning to swim. The intent of this manual is to prepare the learner with the fundamental skills and critical knowledge necessary to enroll in a beginning swim class, to mentally prepare them for the upcoming tasks of learning to swim and to provide a strong foundation for the learner to build on.Includes bibliographical references (leaves 100-101)California State University, Northridge. Department of Kinesiology