Decomposition of tournament limits
arXiv:1604.04271 · doi:10.1016/j.ejc.2017.07.023
Abstract
The theory of tournament limits and tournament kernels (often called graphons) is developed by extending common notions for finite tournaments to this setting; in particular we study transitivity and irreducibility of limits and kernels. We prove that each tournament kernel and each tournament limit can be decomposed into a direct sum of irreducible components, with transitive components interlaced. We also show that this decomposition is essentially unique.
31 pages; 3 figures