AI 中文总结
本文基于Fernau等人的通用框架，研究极小二元语言对区间图等图类的刻画作用，同时证明稀疏图族无法被该方法下的语言刻画，强化了形式语言与图类的联系。
AI 中文摘要
词可表示性的研究始于Kitaev和Pyatkin 2008年的开创性工作，后续催生了Kitaev和Lozin 2015年的专著。本文基于Fernau等人近期提出的通用框架，该框架推广了词可表示性的某些方面，使任意二元语言均可描述一类图。我们系统研究了极小语言，发现其可刻画区间图、置换图、圆图、二部链图等知名图类，从而强化了形式语言与图类的联系，即便对于极小二元语言亦是如此。我们还证明了该方法的局限性，例如平面图等稀疏图族无法被该方法下的任何语言刻画。
英文摘要
The study of word-representability was initiated by the seminal work of Kitaev and Pyatkin in 2008 that has later led to the monograph by Kitaev and Lozin in 2015. In this paper, we build on the very recent work by Fernau et al. who proposed a general framework that generalizes certain aspects of word-representability, so that any binary language describes a graph class. In this work, we systematically study particularly small languages and observe that they characterize well-known graph classes, e.g., interval, permutation, circle, and bipartite chain graphs. Thus, we strengthen the bond between formal languages and graph classes, even for small binary languages. We also show some limitations of our approach by proving that, e.g., families of sparse graphs like planar graphs cannot be characterized by any language following this approach.
CommentsIn Proceedings AFL 2026, arXiv:2608.23071
Journal refEPTCS 451, 2026, pp. 155-170
