相关论文: Simplification & Incidence: How an Incidence-focus…

This paper considers the difficulty in the set-system approach to generalizing graph theory. These difficulties arise categorically as the category of set-system hypergraphs is shown not to be cartesian closed and lacks enough projective…

The simplification of a multigraph into a simple graph can be abstracted to a more general comma category under some common conditions. When using the identity functor, the category of simple objects in a comma category generalizes the…

In the standard Category of Graphs, the graphs allow only one edge to be incident to any two vertices, not necessarily distinct, and the graph morphisms must map edges to edges and vertices to vertices while preserving incidence. We refer…

While lifting map has significantly enhanced the expressivity of graph neural networks, extending this paradigm to hypergraphs remains fragmented. To address this, we introduce the categorical Weisfeiler-Lehman framework, which formalizes…

We continue the study of the recently-introduced C123-framework, for (simple) graph problems restricted to inputs specified by the forbidding of some finite set of subgraphs, to more general graph problems possibly involving multiedges and…

Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…

An oriented hypergraph is an oriented incidence structure that allows for the generalization of graph theoretic concepts to integer matrices through its locally signed graphic substructure. The locally graphic behaviors are formalized in…

The box product and its associated box exponential are characterized for the categories of quivers (directed graphs), multigraphs, set system hypergraphs, and incidence hypergraphs. It is shown that only the quiver case of the box…

We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives…

We present a doctrinal approach to category theory, obtained by abstracting from the indexed inclusions (via discrete fibrations and opfibrations) of the left and of the right actions of X in Cat in categories over X. Namely, a "weak…

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

A graph covering projection, also referred to as a locally bijective homomorphism, is a mapping between the vertices and edges of two graphs that preserves incidences and is a local bijection. This concept originates in topological graph…

A hedge graph is a graph whose edge set has been partitioned into groups called hedges. Here we consider a generalization of the well-known \textsc{Cluster Deletion} problem, named \textsc{Hedge Cluster Deletion}. The task is to compute the…

Detecting anomalies in link streams that represent various kinds of interactions is an important research topic with crucial applications. Because of the lack of ground truth data, proposed methods are mostly evaluated through their ability…

We view hyper-graphs as incidence graphs, i.e. bipartite graphs with a set of nodes representing vertices and a set of nodes representing hyper-edges, with two nodes being adjacent if the corresponding vertex belongs to the corresponding…

Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

We consider two incidence problems for integral curves of vector fields. The first is an analogue of the Euclidean joints problem, in which lines are replaced by integral curves of smooth vector fields taken from some finite-dimensional…

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…

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…