Complete Graphs 2
Each of the edges of a complete graph with 10 vertices is coloured either blue or red .There are x vertices such that all the edges connecting them are of the same colour.
Find x
Details - In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction) (source - Wikipedia)for more go to Wikipedia site
The answer is 4.
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1 solution
You should rewrite the question as: No matter what the colouring of the edges is, there will always be at least x vertices such that the edges connecting all x vertices are either all blue or all red. Find the maximum value of x .
Also, I believe the answer may be 3 and not 4.