This free online book consists of invited surveys of various fields of infinite graph theory and combinatorics, as well as a few research articles. It aims to give some indication of the variety of problems and methods found in this area, but also to help identify what may be seen as its typical features, placing it somewhere between finite graph theory on the one hand and logic and set theory on the other.

## Book Description

This book has arisen from a colloquium held at St. John’s College, Cambridge, in July 1989, which brought together most of today’s leading experts in the field of infinite graph theory and combinatorics. This was the first such meeting ever held, and its aim was to assess the state of the art in the discipline, to consider its links with other parts of mathematics, and to discuss possible directions for future development. This volume reflects the Cambridge meeting in both level and scope. It contains research papers as well as expository surveys of particular areas. Together they offer a comprehensive portrait of infinite graph theory and combinatorics, which should be particularly attractive to anyone new to the discipline.

## Table of Contents

- Infinite matching theory
- Gallai-Milgram properties for infinite graphs
- The age of a relational structure
- Decomposing infinite graphs
- Bounded graphs
- A survey on graph with polynomial growth
- Some results on ends and automorphisms of graphs
- Analysing Nash-Williams’ partition theorem by means of ordinal types
- Matchings from a set below to a set above
- A partition relation for triples using a model of Todorcevic
- Some relations between analytic and geometric properties of infinite graphs
- Reconstruction of infinite graphs
- f-Optimal factors of infinite graphs
- Universal elements and the complexity of certain classes of infinite graphs
- Asymmentrising sets in trees
- Asymmetrization of infinite trees
- Excluding infinite minors
- An end-faithful spanning tree counterexample
- End-faithful forests and spanning trees in infinite graphs
- Fast growing functions based on Ramsey theorems
- Edge transitive strips
- Topological groups and infinite graphs