Related papers: Graph parameters, implicit representations and fac…
Neural approaches to program synthesis and understanding have proliferated widely in the last few years; at the same time graph based neural networks have become a promising new tool. This work aims to be the first empirical study comparing…
Predictive coding is a message-passing framework initially developed to model information processing in the brain, and now also topic of research in machine learning due to some interesting properties. One of such properties is the natural…
An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from all other vertices by the set of vertices in C that are at distance at most 1 from x. The problem of finding an identifying code of…
In this paper, we present a novel implicit glyph shape representation, which models glyphs as shape primitives enclosed by quadratic curves, and naturally enables generating glyph images at arbitrary high resolutions. Experiments on font…
A graph $U$ is an induced universal graph for a family $F$ of graphs if every graph in $F$ is a vertex-induced subgraph of $U$. For the family of all undirected graphs on $n$ vertices Alstrup, Kaplan, Thorup, and Zwick [STOC 2015] give an…
The graph $G$ is said to be strongly regular with parameters $(n,k,\lambda,\mu)$ if the following conditions hold: (1) each vertex has $k$ neighbours; (2) any two adjacent vertices of $G$ have $\lambda$ common neighbours; (3) any two…
In the $(G,H)$-isomorphism game, a verifier interacts with two non-communicating players (called provers) by privately sending each of them a random vertex from either $G$ or $H$, whose aim is to convince the verifier that two graphs $G$…
The Transformer architecture has become a dominant choice in many domains, such as natural language processing and computer vision. Yet, it has not achieved competitive performance on popular leaderboards of graph-level prediction compared…
Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data. Due to the finite nature of the underlying recurrent structure, current GNN methods may struggle to capture…
The girth of a graph is the length of its shortest cycle. Due to its relevance in graph theory, network analysis and practical fields such as distributed computing, girth-related problems have been object of attention in both past and…
Graphs are a fundamental abstraction for modeling relational data. However, graphs are discrete and combinatorial in nature, and learning representations suitable for machine learning tasks poses statistical and computational challenges. In…
We investigate the parameterized complexity of finding subgraphs with hereditary properties on graphs belonging to a hereditary graph class. Given a graph $G$, a non-trivial hereditary property $\Pi$ and an integer parameter $k$, the…
For any hereditary graph class $F$, we construct optimal adjacency labeling schemes for the classes of subgraphs and induced subgraphs of Cartesian products of graphs in $F$. As a consequence, we show that, if $F$ admits efficient adjacency…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
We show that for any constant $\Delta \ge 2$, there exists a graph $G$ with $O(n^{\Delta / 2})$ vertices which contains every $n$-vertex graph with maximum degree $\Delta$ as an induced subgraph. For odd $\Delta$ this significantly improves…
A simple graph G is said to be representable in a real vector space of dimension m if there is an embedding of the vertex set in the vector space such that the Euclidean distance between any two distinct vertices is one of only two distinct…
A family of graphs $\mathcal{F}$ is hereditary if $\mathcal{F}$ is closed under isomorphism and taking induced subgraphs. The speed of $\mathcal{F}$ is the sequence $\{|\mathcal{F}^n|\}_{n \in \mathbb{N}}$, where $\mathcal{F}^n$ denotes the…
Let $k$ be a positive integer and let $G$ be a graph with vertex set $V(G)$. A subset $D \subseteq V(G)$ is a $k$-dominating set if every vertex outside $D$ is adjacent to at least $k$ vertices in $D$. The $k$-domination number…
The recommendation system is not only a problem of inductive statistics from data but also a cognitive task that requires reasoning ability. The most advanced graph neural networks have been widely used in recommendation systems because…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…