Friday, July 24, 2026 11:30 am
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12:30 pm
EDT (GMT -04:00)
Abstract: A family of sets $\mathcal{C}$ over a finite ground set $E(\mathcal{C})$ is a clutter if no member of $\mathcal{C}$ properly contains another. A clutter is ideal if its covering polyhedron is integral. A rational number whose denominator is a power of two is called \emph{dyadic}. A longstanding conjecture of Paul Seymour, known as the Dyadic Conjecture, predicts that, for every ideal clutter, the dual of the set covering linear program admits an optimal solution in which all variables take dyadic values. We present a local version of this conjecture and provide evidence for it by proving the proposed local statement for binary clutters under certain assumptions.
This is joint work with Bertrand Guenin and Levent Tuncel.
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