Related papers: Regular Grammars as Effective Representations of R…
Regular word grammars are restricted context-free grammars that define all the recognizable languages of words. This paper generalizes regular grammars from words to certain classes of graphs, by defining regular grammars for unordered…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
Hyperedge-Replacement grammars (HR) have been introduced by Courcelle in order to extend the notion of context-free sets from words and trees to graphs of bounded tree-width. While for words and trees the syntactic restrictions that…
The literature on word-representable graphs is quite rich, and a number of variations of the original definition have been proposed over the years. We are initiating a systematic study of such variations based on formal languages. In our…
Once the set of finite graphs is equipped with an algebra structure (arising from the definition of operations that generalize the concatenation of words), one can define the notion of a recognizable set of graphs in terms of finite…
In the area of beyond-planar graphs, i.e. graphs that can be drawn with some local restrictions on the edge crossings, the recognition problem is prominent next to the density question for the different graph classes. For 1-planar graphs,…
A class of graph languages is definable in Monadic Second-Order logic (MSO) if and only if it consists of sets of models of MSO formul{\ae}. If, moreover, there is a computable bound on the tree-widths of the graphs in each such set, the…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…
We investigate the structure of conformally rigid graphs. Graphs are conformally rigid if introducing edge weights cannot increase (decrease) the second (last) eigenvalue of the Graph Laplacian. Edge-transitive graphs and distance-regular…
We give a characterization of the sets of graphs that are both definable in Counting Monadic Second Order Logic (CMSO) and context-free, i.e., least solutions of Hyperedge-Replacement (HR) grammars introduced by Courcelle and Engelfriet. We…
Recent research has shown that alignment between the structure of graph data and the geometry of an embedding space is crucial for learning high-quality representations of the data. The uniform geometry of Euclidean and hyperbolic spaces…
Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…
Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…
We investigate the parameterized complexity of the recognition problem for the proper $H$-graphs. The $H$-graphs are the intersection graphs of connected subgraphs of a subdivision of a multigraph $H$, and the properness means that the…
Regular colored graphs are dual representations of pure colored D-dimensional complexes. These graphs can be classified with respect to an integer, their degree, much like maps are characterized by the genus. We analyse the structure of…
A graph $G = (\{1, 2, \ldots, n\}, E)$ is $12$-representable if there is a word $w$ over $\{1, 2, \ldots, n\}$ such that two vertices $i$ and $j$ with $i < j$ are adjacent if and only if every $j$ occurs before every $i$ in $w$. These…
Graph polynomials which are definable in Monadic Second Order Logic (MSOL) on the vocabulary of graphs are Fixed-Parameter Tractable (FPT) with respect to clique-width. In contrast, graph polynomials which are definable in MSOL on the…
This paper describes substantial advances in the analysis (parsing) of diagrams using constraint grammars. The addition of set types to the grammar and spatial indexing of the data make it possible to efficiently parse real diagrams of…