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We study the problems of counting copies and induced copies of a small pattern graph $H$ in a large host graph $G$. Recent work fully classified the complexity of those problems according to structural restrictions on the patterns $H$. In…
Commonly used proof strategies by automated reasoners organise proof search either by ordering-based saturation or by reducing goals to subgoals. In this paper, we combine these two approaches and advocate a SAT-based method with symmetry…
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…
We investigate the decidability and complexity status of model-checking problems on unlabelled reachability graphs of Petri nets by considering first-order and modal languages without labels on transitions or atomic propositions on…
This paper presents new results and reinterpretation of existing conditions for strong structural controllability in a structured network determined by the zero/non-zero patterns of edges. For diffusively-coupled networks with self-loops,…
For a connected graph, a vertex separator is a set of vertices whose removal creates at least two components and a minimum vertex separator is a vertex separator of least cardinality. The vertex connectivity refers to the size of a minimum…
Pattern matching is a fundamental tool for answering complex graph queries. Unfortunately, existing solutions have limited capabilities: they do not scale to process large graphs and/or support only a restricted set of search templates or…
We report on a recent breakthrough in rule-based graph programming, which allows us to reach the time complexity of imperative linear-time algorithms. In general, achieving the complexity of graph algorithms in conventional languages using…
We present a first-order linear-time temporal logic for reasoning about the evolution of directed graphs. Its semantics is based on the counterpart paradigm, thus allowing our logic to represent the creation, duplication, merging, and…
The planar separator theorem by Lipton and Tarjan [FOCS '77, SIAM Journal on Applied Mathematics '79] states that any planar graph with $n$ vertices has a balanced separator of size $O(\sqrt{n})$ that can be found in linear time. This…
Neural networks excel at pattern recognition but struggle with reliable logical reasoning, often violating basic logical principles during inference. We address this limitation by developing a categorical framework that systematically…
The dynamic trees problem is to maintain a forest undergoing edge insertions and deletions while supporting queries for information such as connectivity. There are many existing data structures for this problem, but few of them are capable…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
Let CMSO denote the counting monadic second order logic of graphs. We give a constructive proof that for some computable function $f$, there is an algorithm $\mathfrak{A}$ that takes as input a CMSO sentence $\varphi$, a positive integer…
Kernelization studies polynomial-time preprocessing algorithms. Over the last 20 years, the most celebrated positive results of the field have been linear kernels for classical NP-hard graph problems on sparse graph classes. In this paper,…
In the Survivable Network Design Problem (SNDP), the input is an edge-weighted (di)graph $G$ and an integer $r_{uv}$ for every pair of vertices $u,v\in V(G)$. The objective is to construct a subgraph $H$ of minimum weight which contains…
The canonical tree-decomposition theorem, given by Robertson and Seymour in their seminal graph minors series, turns out to be one of the most important tool in structural and algorithmic graph theory. In this paper, we provide the…
In Two-Sets Cut-Uncut, we are given an undirected graph $G=(V,E)$ and two terminal sets $S$ and $T$. The task is to find a minimum cut $C$ in $G$ (if there is any) separating $S$ from $T$ under the following ``uncut'' condition. In the…
Discrete structure rules for validating molecular structures are usually limited to fulfillment of the octet rule or similar simple deterministic heuristics. We propose a model, inspired by language modeling from natural language…
We present a novel approach to answering sequential questions based on structured objects such as knowledge bases or tables without using a logical form as an intermediate representation. We encode tables as graphs using a graph neural…