On Languages Describing Large Graph Classes

TL;DR

This paper introduces a novel approach to representing large graph classes using formal binary languages, focusing on pattern-based edge definitions and exploring well-known languages like palindromes and Dyck words.

Contribution

It proposes a new formal language-based framework for graph representation, contrasting with previous word-based methods, and investigates specific language restrictions for graph classes.

Findings

Established a new language-based graph representation framework.

Analyzed the use of classical languages like palindromes and Dyck words for graph classes.

Provided insights into how language restrictions affect graph class representation.

Abstract

In this work, we introduce a new notion for representing graph classes with formal languages. In contrast to the seminal work by Kitaev and Pyatkin to represent graphs by words, we use formal binary languages in order to have a set of patterns (given by the languages' words) defining the edges in the graph. In particular, we investigate famous languages like the palindromes, copy-words, Lyndon words, and Dyck words to represent all graphs or specific graph classes by restricting these languages.