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Generalized Pigeonhole Properties of Graphs and Oriented Graphs

✍ Scribed by Anthony Bonato; Peter J Cameron; Dejan Delić; Stéphan Thomassé

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
152 KB
Volume
23
Category
Article
ISSN
0195-6698

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✦ Synopsis

A relational structure A satisfies the P(n, k) property if whenever the vertex set of A is partitioned into n nonempty parts, the substructure induced by the union of some k of the parts is isomorphic to A. The P(2, 1) property is just the pigeonhole property, (P), introduced by Cameron, and studied by Bonato, Delić and Cameron. We classify the countable graphs, tournaments, and oriented graphs with the P(3, 2) property.

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