Related papers: On the Complexity of L-reachability
The Colouring problem asks whether the vertices of a graph can be coloured with at most $k$ colours for a given integer $k$ in such a way that no two adjacent vertices receive the same colour. A graph is $(H_1,H_2)$-free if it has no…
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…
Given a graph $G$ and two vertices $s$ and $t$ in it, {\em graph reachability} is the problem of checking whether there exists a path from $s$ to $t$ in $G$. We show that reachability in directed layered planar graphs can be decided in…
Consider a random graph model where each possible edge $e$ is present independently with some probability $p_e$. Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we…
This paper investigates the computational complexity of deciding whether the vertices of a graph can be partitioned into a disjoint union of cliques and a triangle-free subgraph. This problem is known to be $\NP$-complete on arbitrary…
The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique completability of partially-filled tensors subject to rank…
In the Intersection Non-Emptiness problem, we are given a list of finite automata $A_1,A_2,\dots,A_m$ over a common alphabet $\Sigma$ as input, and the goal is to determine whether some string $w\in \Sigma^*$ lies in the intersection of the…
Large Language Models (LLMs) have achieved impressive results in processing text data, which has sparked interest in applying these models beyond textual data, such as graphs. In the field of graph learning, there is a growing interest in…
Large language models (LLMs) are widely used, but they often generate subtle factual errors, especially in long-form text. These errors are fatal in some specialized domains such as medicine. Existing fact-checking with grounding documents…
This paper investigates the complexity of finding secluded paths in graphs. We focus on the \textsc{Short Secluded Path} problem and a natural new variant we introduce, \textsc{Shortest Secluded Path}. Formally, given an undirected graph…
The problem Cover(H) asks whether an input graph G covers a fixed graph H (i.e., whether there exists a homomorphism G to H which locally preserves the structure of the graphs). Complexity of this problem has been intensively studied. In…
Given an undirected graph $G$, the problem of deciding whether $G$ admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (G\"obel et al., 1991). In this article, we relax this problem and ask…
Graph analysis is fundamental in real-world applications. Traditional approaches rely on SPARQL-like languages or clicking-and-dragging interfaces to interact with graph data. However, these methods either require users to possess high…
Text-attributed graphs (TAGs) enhance graph learning by integrating rich textual semantics and topological context for each node. While boosting expressiveness, they also expose new vulnerabilities in graph learning through text-based…
For any particular class of graphs, algorithms for computational problems restricted to the class often rely on structural properties that depend on the specific problem at hand. This begs the question if a large set of such results can be…
Temporal graphs arise when modeling interactions that evolve over time. They usually come in several flavors, depending on the number of parameters used to describe the temporal aspects of the interactions: time of appearance, duration,…
The connectivity of a graph is an important parameter to evaluate its reliability. $k$-restricted connectivity (resp. $R^h$-restricted connectivity) of a graph $G$ is the minimum cardinality of a set $S$ of vertices in $G$, if exists, whose…
The problem of Distance Edge Labeling is a variant of Distance Vertex Labeling (also known as $L_{2,1}$ labeling) that has been studied for more than twenty years and has many applications, such as frequency assignment. The Distance Edge…
Exploring the application of large language models (LLMs) to graph learning is a emerging endeavor. However, the vast amount of information inherent in large graphs poses significant challenges to this process. This work focuses on the link…
Let $t$ be a positive real number. A graph is called $t$-tough if the removal of any vertex set $S$ that disconnects the graph leaves at most $|S|/t$ components. The toughness of a graph is the largest $t$ for which the graph is $t$-tough.…