MathDB

3

Part of 2015 239 Open Mathematical Olympiad

Problems(2)

Chromatic Bound for a Graph

Source: 239 2015 S P3

5/14/2020
The edges of a graph GG are coloured in two colours. Such that for each colour all the connected components of this graph formed by edges of this colour contains at most n>1n>1 vertices. Prove there exists a proper colouring for the vertices of this graph with nn colours.
graphColoringcombinatorics
coloring of all naturals

Source: 239 2015 J3

5/15/2020
Positive integers are colored either blue or red such that if a,ba,b have the same color and a−10ba-10b is a positive integer then a−10b,aa-10b, a have the same color as well. How many such coloring exist?
combinatorics