Cornell University: Counting Solution Clusters in Graph Coloring Problems

This article is an in-depth look at graphs. Topics covered are graph models, terminology, representations of graphs, graph isomorphism, connectivity, Euler and Hamiltonian Paths, and more. Examples and explanations are included.

Investigating the large numbers of science is the task in a simple but deep activity. Given a one-sentence problem set-up and some basic assumptions, the class sets off on an open-ended investigation that really gives some...

How many ways can you graph a quadratic? The video shows two approaches to graphing a quadratic expression that is initially in standard form. The first method finds the vertex using -b/2a. The second approach is to find (h,k). 

Is the solution really the solution? Given a graph of a linear system, an informative video shows learners how to determine the solution as the point of intersection. The presenter verifies the solution as a solution to the system by...

Solve a pretty straightforward system. Pupils view an educational video showing how to solve a system of linear equations by graphing. The system consists of a horizontal line and a vertical line, making the solution apparent in the...

Find deeper meaning in graphs. Pupils use the knowledge gained from the previous sections in the unit to sketch graphs of a function's derivative. Learners also see how to sketch a graph of a function given the graph of its derivatives....

Sal evaluates a word problem and then solves by graphing systems of equations. This problem would be great as a daily challenge, as concept review, or as a homework assignment. Show this video only after the students have had a chance to...

Graph coloring problem is to assign colors to certain elements of a graph subject to certain constraints. This source looks at different applications of graph coloring.

Kick off the school year with some math fun! New classmates share information about themselves by using graphs and interpreting data. The goal is to use a general graph shape, such as linear or exponential, and create labels for the axes...

Graph coloring is widely used. Unfortunately, there is no efficient algorithm available for coloring a graph with a minimum number of colors as the problem is a known NP-Complete problem. There are approximate algorithms to solve the...