The Structure of Hereditary Properties and Colourings of Random Graphs
✍ Scribed by Béla Bollobás; Andrew Thomason
- Publisher
- Springer-Verlag
- Year
- 2000
- Tongue
- English
- Weight
- 418 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0209-9683
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract A hereditary property of combinatorial structures is a collection of structures (e.g., graphs, posets) which is closed under isomorphism, closed under taking induced substructures (e.g., induced subgraphs), and contains arbitrarily large structures. Given a property $\cal {P}$, we write
Given a property P of graphs, write P n for the set of graphs with vertex set [n] having property P. The growth or speed of a property P can be discussed in terms of the values of |P n |. For properties with |P n | <n n hereditary properties are surprisingly well determined by their speeds. Sharpeni
A class of graphs is hereditary if it is closed under taking induced subgraphs. Classes associated with graph representations have "composition sequences" and we show that this concept is equivalent to a notion of "amalgamation" which generalizes disjoint union of graphs. We also discuss how general