Hypergraphs that are tight for Ryser's conjecture

(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.
  • 5 with 22 edges
  • 42240 with 23 edges (4Mb)
  • 1072050 with 24 edges (96Mb)
  • 150919 with 25 edges (14Mb)
  • 55 with 26 edges
• 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.
  • 833 with 22 edges
  • 2146789 with 23 edges (177Mb)
  • There are 24646668 with 24 edges, which even gzipped would be 2.1Gb, so haven't stored them here.
  • 1001933 with 25 edges (91Mb)
  • 1835 with 26 edges
  • 10 with 27 edges
  • 2 with 28 edges
• 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.

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