Related papers: Characterization of Word-Representable Graphs usin…
We introduces the umodules, a generalisation of the notion of graph module. The theory we develop captures among others undirected graphs, tournaments, digraphs, and $2-$structures. We show that, under some axioms, a unique decomposition…
We prove that a large family of graphs which are decomposable with respect to the modular decomposition can be reconstructed from their collection of vertex-deleted subgraphs.
A transitive decomposition of a graph is a partition of the edge or arc set giving a set of subgraphs which are preserved and permuted transitively by a group of automorphisms of the graph. In this paper we give some background to the study…
Distinct letters $x$ and $y$ alternate in a word $w$ if after deleting in $w$ all letters but the copies of $x$ and $y$ we either obtain a word of the form $xyxy\cdots$ (of even or odd length) or a word of the form $yxyx\cdots$ (of even or…
We consider word maps and word maps with constants on a simple algebraic group. We present results on the images of such maps, in particular, we prove a theorem on the dominance of general word maps with constants, which can be viewed as an…
This paper introduces the notion of involution module, the first generalization of the modular decomposition of 2-structure which has a unique linear-sized decomposition tree. We derive an O(n^2) decomposition algorithm and we take…
Many models learn representations of knowledge graph data by exploiting its low-rank latent structure, encoding known relations between entities and enabling unknown facts to be inferred. To predict whether a relation holds between…
The bipartition polynomial of a graph is a generalization of many other graph polynomials, including the domination, Ising, matching, independence, cut, and Euler polynomial. We show in this paper that it is also a powerful tool for proving…
This paper proposes a learning model, based on rank-fusion graphs, for general applicability in multimodal prediction tasks, such as multimodal regression and image classification. Rank-fusion graphs encode information from multiple…
One major deficiency of most semantic representation techniques is that they usually model a word type as a single point in the semantic space, hence conflating all the meanings that the word can have. Addressing this issue by learning…
A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…
A graph G=(V,E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x,y) is in E for each x not equal to y. The motivation to study representable graphs came from algebra,…
The use of symbolic knowledge representation and reasoning as a way to resolve the lack of transparency of machine learning classifiers is a research area that lately attracts many researchers. In this work, we use knowledge graphs as the…
In this paper we resolve the complexity of the isomorphism problem on all but finitely many of the graph classes characterized by two forbidden induced subgraphs. To this end we develop new techniques applicable for the structural and…
The partial representation extension problem is a recently introduced generalization of the recognition problem. A circle graph is an intersection graph of chords of a circle. We study the partial representation extension problem for circle…
Representing and exploiting multivariate signals requires capturing relations between variables, which we can represent by graphs. Graph dictionaries allow to describe complex relational information as a sparse sum of simpler structures,…
Motivated by the definition of the edge elimination polynomial of a graph we define the covered components polynomial counting spanning subgraphs with respect to their number of components, edges and covered components. We prove a…
Today we have a good theoretical understanding of the representational power of Graph Neural Networks (GNNs). For example, their limitations have been characterized in relation to a hierarchy of Weisfeiler-Lehman (WL) isomorphism tests.…
A graph $G = (V, E)$ is said to be word-representable if a word $w$ can be formed using the letters of the alphabet $V$ such that for every pair of vertices $x$ and $y$, $xy \in E$ if and only if $x$ and $y$ alternate in $w$. A…
We present a new graph compressor that works by recursively detecting repeated substructures and representing them through grammar rules. We show that for a large number of graphs the compressor obtains smaller representations than other…