Related papers: Graph Parameters, Universal Obstructions, and WQO
In this paper, we address problems related to parameters concerning edge mappings of graphs. Inspired by Ramsey's Theorem, the quantity $m(G, H)$ is defined to be the minimum number $n$ such that for every $f: E(K_n) \rightarrow E(K_n)$…
We give an algorithmic and lower-bound framework that facilitates the construction of subexponential algorithms and matching conditional complexity bounds. It can be applied to intersection graphs of similarly-sized fat objects, yielding…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
Graph Transformers (GTs) have recently demonstrated remarkable performance across diverse domains. By leveraging attention mechanisms, GTs are capable of modeling long-range dependencies and complex structural relationships beyond local…
Recent efforts leverage Large Language Models (LLMs) for modeling text-attributed graph structures in node classification tasks. These approaches describe graph structures for LLMs to understand or aggregate LLM-generated textual attribute…
We define a general variant of the graph clustering problem where the criterion of density for the clusters is (high) connectivity. In {\sc Clustering to Given Connectivities}, we are given an $n$-vertex graph $G$, an integer $k$, and a…
Given a graph $G=(V,E)$, a set $\mathcal{F}$ of forbidden subgraphs, we study $\mathcal{F}$-Free Edge Deletion, where the goal is to remove minimum number of edges such that the resulting graph does not contain any $F\in \mathcal{F}$ as a…
Elek and Lippner (2010) showed that the convergence of a sequence of bounded-degree graphs implies the existence of a limit for the proportion of vertices covered by a maximum matching. We provide a characterization of the limiting…
Graph Neural Networks (GNNs) achieve strong performance on node classification tasks but remain difficult to interpret, particularly with respect to which input features drive their predictions. Existing global GNN explainers operate at the…
In recent work by Johnson et al. (2022), a framework was described for the study of graph problems over classes specified by omitting each of a finite set of graphs as subgraphs. If a problem falls into the framework then its computational…
A framework is a graph and a map from its vertices to E^d (for some d). A framework is universally rigid if any framework in any dimension with the same graph and edge lengths is a Euclidean image of it. We show that a generic universally…
Traditionally, graph neural networks have been trained using a single observed graph. However, the observed graph represents only one possible realization. In many applications, the graph may encounter uncertainties, such as having…
We suggest a general oracle-based framework that captures different parallel stochastic optimization settings described by a dependency graph, and derive generic lower bounds in terms of this graph. We then use the framework and derive…
We propose a nonparametric framework for the analysis of networks, based on a natural limit object termed a graphon. We prove consistency of graphon estimation under general conditions, giving rates which include the important practical…
We relativise the Thomassen--Woess definition of accessibility in graphs, defining what it means for a graph to be accessible relative to a peripheral system. In the case of locally finite, quasi-transitive graphs, we characterise relative…
Word-representable graphs, characterized by the existence of a semi-transitive orientation, form a well-studied class of graphs. Comparability graphs form another well-studied class and constitute a subclass of word-representable graphs.…
Given a graph, a $k$-plex is a set of vertices in which each vertex is not adjacent to at most $k-1$ other vertices in the set. The maximum $k$-plex problem, which asks for the largest $k$-plex from the given graph, is an important but…
In this paper, we study the graph classification problem from the graph homomorphism perspective. We consider the homomorphisms from $F$ to $G$, where $G$ is a graph of interest (e.g. molecules or social networks) and $F$ belongs to some…
We initiate the study of a new parameterization of graph problems. In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an…
We consider the problem of finding a Hamiltonian path with precedence constraints in the form of a partial order on the vertex set. This problem is known as Partially Ordered Hamiltonian Path Problem (POHPP). Here, we study the complexity…