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Stability of Hereditary Graph Classes Under Closure Operations

✍ Scribed by Mirka Miller; Joe Ryan; Zdeněk Ryjáček; Jakub Teska; Petr Vrána

Book ID
115558804
Publisher
John Wiley and Sons
Year
2012
Tongue
English
Weight
999 KB
Volume
74
Category
Article
ISSN
0364-9024

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A hereditary property of graphs is a class of graphs which is closed under taking induced subgraphs. For a hereditary property \(\mathscr{P}\), let \(\mathscr{P}_{n}\) denote the set of \(\mathscr{P}\) graphs on \(n\) labelled vertices. Clearly we have \(0 \leqslant\left|\mathscr{P}_{n}\right| \leqs

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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