For every finite m and n there is a finite set {G 1 , . . . , G l } of countable (m β’ K n )-free graphs such that every countable (m β’ K n )-free graph occurs as an induced subgraph of one of the graphs G i .
Universality among graphs omitting a complete bipartite graph
β Scribed by Saharon Shelah
- Book ID
- 118786684
- Publisher
- Springer-Verlag
- Year
- 2012
- Tongue
- English
- Weight
- 428 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0209-9683
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π SIMILAR VOLUMES
For two integers a and b, we say that a bipartite graph G admits an (a, b)bipartition if G has a bipartition (X, Y ) such that |X| = a and |Y | = b. We say that two bipartite graphs G and H are compatible if, for some integers a and b, both G and H admit (a, b)-bipartitions. In this paper, we prove
We study complete Kp,q-factorisations of Kin, n, Simple necessary conditions are found and we conjecture that these conditions are also sufficient. A general construction is given to find infinite families of factorisations proving the conjecture in many cases. The conjecture is proved for Kl,q-fact