相关论文: Typestate Checking and Regular Graph Constraints
Similarity notions between vertices in a graph, such as structural and regular equivalence, are one of the main ingredients in clustering tools in complex network science. We generalise structural and regular equivalences for undirected…
An edge colouring of a graph is called distinguishing if there is no non-trivial automorphism which preserves it. We prove that every at most countable, finite or infinite, connected regular graph of order at least $7$ admits a…
Previous work has suggested that the structural restrictions of graphs from classes of bounded expansion--locally dense pockets in a globally sparse graph--naturally coincide with common properties of real-world networks such as clustering…
In this paper, we introduce a generalization of graphlets to heterogeneous networks called typed graphlets. Informally, typed graphlets are small typed induced subgraphs. Typed graphlets generalize graphlets to rich heterogeneous networks…
So far, a very large amount of work in Natural Language Processing (NLP) rely on trees as the core mathematical structure to represent linguistic informations (e.g. in Chomsky's work). However, some linguistic phenomena do not cope properly…
When using graphs and graph transformations to model systems, consistency is an important concern. While consistency has primarily been viewed as a binary property, i.e., a graph is consistent or inconsistent with respect to a set of…
For a degree sequence, we define the set of edges that appear in every labeled realization of that sequence as forced, while the edges that appear in none as forbidden. We examine structure of graphs whose degree sequences contain either…
We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set…
A graph $G$ covers a graph $H$ if there exists a locally bijective homomorphism from $G$ to $H$. We deal with regular covers where this homomorphism is prescribed by the action of a semiregular subgroup of $\textrm{Aut}(G)$. We study…
In this paper, our goal is to characterize two graph classes based on the properties of minimal vertex (edge) separators. We first present a structural characterization of graphs in which every minimal vertex separator is a stable set. We…
The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
The correctness of many algorithms and data structures depends on reachability properties, that is, on the existence of chains of references between objects in the heap. Reasoning about reachability is difficult for two main reasons. First,…
We establish that every monadic second-order logic (MSO) formula on graphs with bounded treedepth is decidable in a constant number of rounds within the CONGEST model. To our knowledge, this marks the first meta-theorem regarding…
Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures called graphons and graphings. These approach have been unified and generalized by authors in a…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
Model-driven software engineering is a suitable method for dealing with the ever-increasing complexity of software development processes. Graphs and graph transformations have proven useful for representing such models and changes to them.…
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…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…