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Research Article Open access CC BY 4.0

Overview of Graph Colouring and some Ramsey-type Numbers

Benjamin Fraser, Tzvetalin S. Vassilev

Journal of Advances in Mathematics and Computer Science · pp. 414–428 · Published 14 Nov 2014

10.9734/BJMCS/2015/14231

Abstract

We introduce the concept of graph colouring and discuss some classical results in this area. In particular, we consider the problem of finding the minimal graphs, complete or not, whose vertex or edge colouring contains or avoids certain subgraphs. This is generally known as Ramsey theory. We give short proofs of some elementary results in this area, and discuss their relationship to colouring integer sequences.

Graph theory graph colouring critical graphs extremal graphs Ramsey numbers.

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