Papers › Using SAT to study plane Hamiltonian substructures in simple drawings

Using SAT to study plane Hamiltonian substructures in simple drawings

16 May 2023arXiv:2305.09432links table onlyarchive 2025-07-28

Helena Bergold, Stefan Felsner, Meghana M. Reddy, Manfred Scheucher

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In 1988 Rafla conjectured that every simple drawing of a complete graph Kₙ contains a plane, i.e., non-crossing, Hamiltonian cycle. The conjecture is far from being resolved. The lower bounds for plane paths and plane matchings have recently been raised to (logn)¹⁻ᵒ⁽¹⁾ and Ω(√(n)), respectively. We develop a SAT framework which allows the study of simple drawings of Kₙ. Based on the computational data we conjecture that every simple drawing of Kₙ contains a plane Hamiltonian subgraph with 2n-3 edges. We prove this strengthening of Rafla's conjecture for convex drawings, a rich subclass of simple drawings. Our computer experiments also led to other new challenging conjectures regarding plane substructures in simple drawings of complete graphs.

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