Title: Ideal clutters and k-wise intersecting families
|Affiliation:||Carnegie Mellon University|
A clutter is *ideal* if the corresponding set covering polyhedron has no fractional vertices, and it is *k-wise intersecting* if the members don’t have a common element but every k members do. We conjecture that there is a constant k such that every k-wise intersecting clutter is non-ideal.
I will show how this conjecture for k=4 would be an extension of Jaeger’s 8-flow theorem, and how a variation of the conjecture for k=3 would be an extension of Tutte’s 4-flow conjecture. I will also discuss connections to tangential 2-blocks, binary projective geometries, the sums of circuits property, etc.
Joint work with Gerard Cornuejols and Dabeen Lee.
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