Answer to Question #270910 in Combinatorics | Number Theory for vikash

Question #270910

Define K-edge colouring and K-vertex colouring of a graph. Find the edge chromatic numbers to colour the edges of the complete graph with four and five vertices


1
Expert's answer
2021-11-30T16:45:55-0500

Edge coloring of a graph is an assignment of "colors" to the edges of the graph so that no two incident edges have the same color.

An edge coloring with k different colors is called a k-edge-coloring.

A proper k-vertex coloring of a simple graph G = (V,E) is defined as a vertex coloring from a set of k colors such that no two adjacent vertices share a common color.


Edge chromatic number is the number of distinct colors in a minimum edge coloring.

Chromatic number of complete graph Kn is n

So,

for complete graph with four vertices chromatic number is 4

for complete graph with five vertices chromatic number is 5


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