# Extra pearls in graph theory

## TL;DR

This supplement provides additional insights and topics in graph theory, expanding on foundational concepts with discussions on advanced theories, methods, and specific graph classes.

## Contribution

It introduces new discussions and perspectives on various advanced topics in graph theory not covered in the original textbook.

## Key findings

- Enhanced understanding of graph polynomials and generating functions
- New insights into toroidal graphs and the Rado graph
- Extended coverage of probabilistic and algebraic methods in graph theory

## Abstract

This is a supplement for "Pearls in graph theory" -- a textbook written by Nora Hartsfield and Gerhard Ringel. We discuss the following topics: Ramsey theory, Probabilistic method, Deletion-contraction formulas, Matrix theorem, Graph-polynomials, Generating functions, Minimum spanning trees, Marriage theorem and its relatives, Toroidal graphs, Rado graph, Rewriting systems.