DM.3† planar graph has a chromatic number that is less than or equal to The student will use problem solving, mathematical communication, four (the four-color-map theorem). mathematical reasoning, connections, and representations to A graph can be colored with two colors if and only if it contains no Model projects consisting of several subtasks, using a graph. cycle of odd length. Use graphs to resolve conflicts that arise in scheduling. The chromatic number of a graph cannot exceed one more than the Determine the chromatic number of a graph. maximum number of degrees of the vertices of the graph. Standard should be included in a one-semester course in Discrete Mathematics. †
DM.3† planar graph has a chromatic number that is less than or equal to four (the four-color-map theorem). A graph can be colored with two colors if and only if it contains no cycle of odd length. The chromatic number of a graph cannot exceed one more than the maximum number of degrees of the vertices of the graph. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Model projects consisting of several subtasks, using a graph. Use graphs to resolve conflicts that arise in scheduling. Determine the chromatic number of a graph. † Standard should be included in a one-semester course in Discrete Mathematics.