Unpacked Content
Knowledge
Students know:
- Graphing procedures and properties.
Skills
Students are able to:
- Model application-based problems that may be solved using graph colorings.
- Color the edges or vertices of a graph using the least number of colors so that no two adjacent vertices or edges are colored the same.
- Interpret the coloring of the graph in terms of a solution for an application-based problem, such as scheduling committee meetings (vertex colorings) or class scheduling (edge-colorings).
- Identify structures in a graph that require a minimum number of colors for a proper coloring.
Understanding
Students understand that:
- -Techniques are used to minimize colors needed to color the vertices (edges) of a graph so that no two adjacent vertices (edges) are colored the same. -Real-world problems such as scheduling and conflict can be modeled with graphs and solved using the minimization of the number of colors.
Vocabulary
- Vertex coloring
- Matching techniques
- Conflict graphs
- Adjacent edges
- Adjacent vertices
- Odd wheel graph
- Proper coloring
