Random 0/1 polytopes have edge-expansion Θ(d) whp for p ≤ 1-ε and Ω(d^k) for any k when p ≤ 1/2-ε, verifying the Mihail-Vazirani conjecture in strong form with a phase transition at p=1/2.
Proceedings of the London Mathematical Society , volume=
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Two novel neighborhood structures for incomplete round-robin tournament scheduling are introduced, with one proven to connect the full solution space, leading to new best solutions via an adaptive late acceptance hill-climbing algorithm.
R(K_{2,n}, C_m) equals m+1 for m at least 3n+4, proving C_m is K_{2,n}-good in this range, with a disproof for even m when n is at least m+2.
Iterative cutting-plane generation and arc preprocessing reduce TSP model size and yield performance gains on classical, direct quantum, and hybrid D-Wave solvers.
citing papers explorer
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The Mihail-Vazirani conjecture and strong edge-expansion in random $0/1$ polytopes
Random 0/1 polytopes have edge-expansion Θ(d) whp for p ≤ 1-ε and Ω(d^k) for any k when p ≤ 1/2-ε, verifying the Mihail-Vazirani conjecture in strong form with a phase transition at p=1/2.
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Novel neighborhood structures for incomplete round robin sports tournaments
Two novel neighborhood structures for incomplete round-robin tournament scheduling are introduced, with one proven to connect the full solution space, leading to new best solutions via an adaptive late acceptance hill-climbing algorithm.
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On Ramsey goodness of $K_{2,n}$ versus cycles
R(K_{2,n}, C_m) equals m+1 for m at least 3n+4, proving C_m is K_{2,n}-good in this range, with a disproof for even m when n is at least m+2.
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Cutting-plane methodology via quantum optimization for solving the Traveling Salesman Problem
Iterative cutting-plane generation and arc preprocessing reduce TSP model size and yield performance gains on classical, direct quantum, and hybrid D-Wave solvers.