Abstract
Let κ be a successor cardinal. We prove that consistently every bipartite graph of size κ + × κ + contains either an independent set or a clique of size τ × τ for every ordinal τ < κ + . We prove a similar theorem for ℓ-partite graphs.
| Original language | English |
|---|---|
| Pages (from-to) | 99-106 |
| Number of pages | 8 |
| Journal | Order |
| Volume | 36 |
| Issue number | 1 |
| DOIs | |
| State | Published - 15 Mar 2019 |
Bibliographical note
Publisher Copyright:© 2018, Springer Science+Business Media B.V., part of Springer Nature.
Keywords
- Bipartite graph
- Polarized relation
- Saturated ideals