Map Coloring
Vertex Drawing
Txt: mini excursion 2 (p. 318-330 )
& SOL: DM.1
Classwork
Project Assigned due in two blocks
(print the rubric at the end of the power point slide)
Apply the Four Color Theorem to one of the graphs
Homework (day 52)
worksheet
A Graph is a collection of points (or circles) some of which are
joined by lines or curves. These are called “vertices” and “edges.”
The word node is sometimes used instead of “vertex”;
the word arc is sometimes used in place of “edge.”
Each edge joins two different vertices. A given pair of
vertices may or may not be joined by an edge.
Coloring of a Map involved assigning colors to the countries
of a map so that Countries with a common border are assigned
different colors.
“Coloring of a graph” involves assigning colors to the vertices
of a graph so that adjacent vertices are assigned different colors.
The “Chromatic number of a graph” is the smallest number of colors that can be
Used for a coloring of the graph. If the graph is called 𝐺, then the chromatic
number
of 𝐺 is often written χ(𝐺), where 𝜒 is the Greek letter, “Chi” (read Kye).
A complete graph is a graph in which every vertex is adjacent to every other
vertex.
A cycle is a graph where the vertices can be arranged in a circular fashion so
that each vertex is adjacent to the two vertices which come before and after it
in the circle.
An Edge (arc) is a line segment whose
end points are vertices in a graph.
The Valence is the number of edges
ending at an end point.
Map Coloring
https://www.youtube.com/watch?v=ANY7X-_wpNs
• A “coloring of a map” involves assigning colors to the countries
of a map so that countries with a common border are assigned
different colors.
• Vertex coloring of graphs can be used to solve a variety of
problems which involve “conflict.” In a situation involving maps,
two countries are in conflicting if they share the same border.
We resolve the conflict by assigning conflicting countries
different colors. In a situation involving class projects, two
projects are in conflict if they share the same member. We
resolve the conflict by assigning conflicting projects different
meeting times.
• Edge colorings of graph can be used to schedule tournaments,
especially round robin.
“The Story of the Young Map Color-er”