AI 中文总结
本文以弦性为参数明确双分图哈密顿性的P与NP完全二分结论，强化相关研究并求解其变体，为该领域提供了关键二分结果。
AI 中文摘要
连通图G称为双分图，若其顶点集可划分为一个稳定集和一个完全二分图。我们以弦性为参数建立如下二分结论：弦双分图的哈密顿环（HCYCLE）和哈密顿路径（HPATH）问题可在多项式时间内求解；弦二分双分图的HCYCLE（HPATH）是NP完全的。我们进一步强化文献[1]的结果，证明HCYCLE（HPATH）在不含P5的弦二分图（二分链图）上可多项式时间求解，在不含P10的弦二分图上为NP完全。以HCYCLE（HPATH）的多项式结果为框架，我们还求解了HCYCLE（HPATH）的多个变体与推广问题，相关结果均在本文中报告。
英文摘要
A connected graph G is said to be a bisplit graph if the vertex set of G can be partitioned into a stable set and a complete bipartite graph. We establish the following dichotomy with chordality being the parameter; for chordal bisplit graphs, Hamiltonian cycle (HCYCLE) and Hamiltonian path (HPATH) problems are polynomial-time solvable, and for chordal bipartite bisplit graphs, HCYCLE (HPATH) is NP-complete. We further strengthen the result of [1] and show that HCYCLE (HPATH) is polynomial-time solvable on P5-free chordal bipartite graphs (bipartite chain graphs) and NP-complete on P10-free chordal bipartite graphs. By using our polynomial results on HCYCLE (HPATH) as a framework, we solve many variants and generalizations of HCYCLE (HPATH), which are also reported in this paper.
