# Combinatorics/Graph & Ramsey Theory

**Welcome to the Lesson of Graph & Ramsey Theory**

In mathematics and computer science, **graph theory** is the study of *graphs*: mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of 'vertices' or 'nodes' and a collection of *edges* that connect pairs of vertices. A graph may be *undirected*, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be *directed* from one vertex to another. The graphs studied in graph theory should not be confused with "graphs of functions" and other kinds of graphs.

## Theorems[edit | edit source]

Ramsey's Theorem is the solution to the Party Planner Problem

Schur's Theorem is a central theorem in Ramsey theory and combinatorial number theory that is concerned with arithmetic progressions.

Van der Waerden's Theorem is another theorem that is concerned with arithmetic progressions on the integers.

## Sudoku[edit | edit source]

## Colouring Problems[edit | edit source]

## See Also[edit | edit source]

- Wikipedia: Ramsey theory
- Wikipedia: Ramsey's theorem
- Wikipedia: Schur's lemma
- Wikipedia: Van der Waerden's theorem