MathDB

Here

G_{n}

denotes a simple undirected graph with

n

vertices,

K_{n}

denotes the complete graph with

n

vertices,

K_{n,m}

the complete bipartite graph whose components have

m

and

n

vertices, and

C_{n}

a circuit with

n

vertices. The number of edges in the graph

G_{n}

is denoted

e(G_{n})

. The edges of

K_{n}(n \geq 3)

are colored with

n

colors, and every color is used. Show that there is a triangle whose sides have different colors.

Problem Statement