The classical theorem of Vizing states that every graph of maximum degree d admits an edge-coloring with at most d + 1 colors. Furthermore, as it was earlier shown by Kőnig, d colors suffice if the graph is bipartite. We investigate the existence of measurable edge-colorings for graphings. A graphing is an analytic generalization of a bounded-degree graph that appears in various areas, such as ...

By permitting students to experiment with “new” forms of learning and “seeing” mathematics, graphing calculators affect the learning process and, as a consequence, can put pressure on teachers and curriculum developers concerning the teaching process. In this way, when adequate conditions are given, this new technology can reinforce the change process that is taking place in the teaching and le...

One of the strengths of a graphics calculator is the potential it offers for students to explore mathematical ideas from a few different perspectives. A good example of this involves the normal probability distribution, frequently encountered in senior secondary courses involving statistics. This note describes a few ways in which the Casio cfx-9850G series of calculators can be used to evaluat...

Identify the domain and range of each. Then sketch the graph.

The increasing size of Big Data is often heralded but how data are transformed and represented is also profoundly important to knowledge discovery, and this is exemplified in Big Graph analytics. Much attention has been placed on the scale of the input graph but the product of a graph algorithm can be many times larger than the input. This is true for many graph problems, such as listing all tr...

The Journal of the American Osteopathic Association May 2013 | Vol 113 | No. 5 424 Statistical Figures (Graphs) For statistical figures, authors must choose a graphing format appropriate for the type of relationship they would like to communicate. For example, line graphs are appropriate for showing trends, and bar graphs are appropriate for showing magnitudes. Below, I describe common graphing...