AI 中文总结
该研究通过将3-SAT直接归约到非平面图的无交叉哈密顿路径与环问题，分离了哈密顿问题与无交叉约束的难度，得到更清晰的难解性证明，便于推广到相关问题。
AI 中文摘要
我们通过将3-SAT问题直接归约到非平面图上的无交叉哈密顿路径与环问题，来分离寻找哈密顿路径或环的难度与寻找无交叉路径或环的难度。此前的难解性证明通过归约到平面图进行，而平面图中每条路径自动无交叉，这混淆了两种难度来源，且未明确为何仅禁止路径上的交叉会使问题变难。我们的归约将难度完全归于无交叉约束，避免了平面小工具构造，得到了更清晰的证明，可能更易于推广到相关问题。
英文摘要
We seek to disentangle the hardness of finding a Hamiltonian path or cycle from the hardness of finding a non-crossing path or cycle by giving a direct reduction from 3-SAT to the non-crossing Hamiltonian path and cycle problems on non-planar graphs. Prior hardness proofs proceed by reduction to planar graphs, where every path is automatically non-crossing; this conflates the two sources of difficulty and leaves unclear why forbidding crossings on the path alone makes the problem hard. Our reduction places the difficulty squarely in the non-crossing constraint, avoids planar gadget constructions, and yields a more transparent proof that may be easier to extend to related problems.
