Hypergraphs that are tight for Ryser's conjecture
Examples for the paper N.Francetić, S.Herke, B.D.McKay and I.M.Wanless,
On Ryser's conjecture for linear intersecting multipartite hypergraphs,
European J. Combin.
(Some of this data was produced by my coauthor Brendan McKay)
Most of what we present on this page is some 8-partite intersecting
hypergraphs that have covering number τ=7 and hence are tight for
Ryser's conjecture. The format is that each line in a file represents
one hypergraph. Each word represents one edge, with the i-th letter
saying which vertex on side i the edge hits.
- The hypergraph H38 as described in the paper.
- The 5 smallest subhypergraphs of H38 that have τ=7.
(Vertices on the last side have been renumbered to remove gaps.)
- Edge minimal subhypergraphs of H38 that have τ=7:
These have been relabelled, so are given only up to isomorphism.
- Edge minimal subhypergraphs of the punctured projective plane of order 7
that have τ=7:
Again, these have been relabelled, so are given only up to isomorphism.
- Finally there's a 13-partite intersecting
hypergraph with τ=12, as described in the paper. This was the
first example known to achieve equality in Ryser's conjecture for r=13.
Back to data homepage.