EdgeChromaticNumber
gives the chromatic number for the edges of the graph g.
Details and Options
- EdgeChromaticNumber is also known as chromatic index.
- EdgeChromaticNumber gives the smallest number of colors that can be assigned to the edges of the graph g such that no two adjacent edges have the same color.
Examples
open all close allBasic Examples (2)
Scope (6)
EdgeChromaticNumber works with undirected graphs:
Use rules to specify the graph:
EdgeChromaticNumber works with large graphs:
Applications (2)
Tournament Schedule (2)
To schedule a round-robin tournament, build a graph where vertices correspond to the competitors in the tournament and the edges correspond to games:
Find at least how many rounds need to be scheduled so that each pair of competitors plays each other in one of the rounds:
In the National Football League, the pairs of teams that will play each other in a given year are determined based on the teams' records from the previous year. Build a graph where vertices correspond to the teams and the edges correspond to games:
Properties & Relations (5)
The chromatic index for a cycle graph is 2 when it has an even number of vertices; otherwise it is 3:
The chromatic index for a wheel graph is one less than the number of vertices:
Using FindEdgeColoring to compute EdgeChromaticNumber:
The chromatic index for a simple graph is either its maximum degree 
or 
:
The chromatic index for a bipartite graph is its maximum degree:
Text
Wolfram Research (2021), EdgeChromaticNumber, Wolfram Language function, https://reference.wolfram.com/language/ref/EdgeChromaticNumber.html.
CMS
Wolfram Language. 2021. "EdgeChromaticNumber." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EdgeChromaticNumber.html.
APA
Wolfram Language. (2021). EdgeChromaticNumber. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EdgeChromaticNumber.html