Problem
COM-B2-M06-P001 Five Edges from One Vertex
#1
★★☆☆☆ Level 2 of 5
From a vertex of the complete graph on \(6\) vertices, \(5\) edges leave, each red or blue. Prove that among them there are \(3\) edges of the same colour.
Distribute five edges between two colours.
If there are at most \(2\) red edges and at most \(2\) blue edges, then there are at most \(4\) edges in total. But there are \(5\). Hence at least one colour appears at least \(3\) times.
A basic technical lemma for \(R(3,3)\).