Language-Representability: Possibilities and Limitations

2026-08-25

AI Summary

研究通过扩展二进制语言框架，探讨了小语言如何描述已知图类，并指出该方法在表征稀疏图（如平面图）时的局限性。

Abstract

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.

Problem

• word-representability
• graph classes
• binary languages
• formal languages

Innovation

• word-representability
• binary language
• graph class
• formal languages
• sparse graphs