Related papers: Counting unlabelled multigraphs with three nodes
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
A graph coloring has bounded clustering if each monochromatic component has bounded size. This paper studies such a coloring, where the number of colors depends on an excluded complete bipartite subgraph. This is a much weaker assumption…
Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a 3-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily 3-connected i.e. the sequence…
We explore the application of graph coloring to biological networks, specifically protein-protein interaction (PPI) networks. First, we find that given similar conditions (i.e. number of nodes, number of links, degree distribution and…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
Laman graphs naturally arise in structural mechanics and rigidity theory. Specifically, they characterize minimally rigid planar bar-and-joint systems which are frequently needed in robotics, as well as in molecular chemistry and polymer…
Polytopes from subgraph statistics are important in applications and conjectures and theorems in extremal graph theory can be stated as properties of them. We have studied them with a view towards applications by inscribing large explicit…
This paper deals with graph classes characterization and recognition. A popular way to characterize a graph class is to list a minimal set of forbidden induced subgraphs. Unfortunately this strategy usually does not lead to an efficient…
For a flexible labeling of a graph, it is possible to construct infinitely many non-equivalent realizations keeping the distances of connected points constant. We give a combinatorial characterization of graphs that have flexible labelings.…
This extended abstract introduces a class of graph learning applicable to cases where the underlying graph has polytopic uncertainty, i.e., the graph is not exactly known, but its parameters or properties vary within a known range. By…
Graph neural networks (GNNs) have achieved superior performance on node classification tasks in the last few years. Commonly, this is framed in a transductive semi-supervised learning setup wherein the entire graph, including the target…
We characterize the compatibility of a collection of unrooted phylogenetic trees as a question of determining whether a graph derived from these trees --- the display graph --- has a specific kind of triangulation, which we call legal. Our…
An explicit algorithm is presented for testing whether two non-directed graphs are isomorphic or not. It is shown that for a graph of n vertices, the number of n independent operations needed for the test is polynomial in n. A proof that…
Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…
In the past, the dichotomy between homophily and heterophily has inspired research contributions toward a better understanding of Deep Graph Networks' inductive bias. In particular, it was believed that homophily strongly correlates with…
In this paper we extend the theory of bidimensionality to two families of graphs that do not exclude fixed minors: map graphs and power graphs. In both cases we prove a polynomial relation between the treewidth of a graph in the family and…
The simple connected graphs may be classified by their cycle composition (number and lengths of cycles). This work derives the counting series of the simple connected graphs that have cycles of unrestricted number and length, but no…
We examine two fundamental tasks associated with graph representation learning: link prediction and node classification. We present a new autoencoder architecture capable of learning a joint representation of local graph structure and…
Hypergraphs, which belong to the family of higher-order networks, are a natural and powerful choice for modeling group interactions in the real world. For example, when modeling collaboration networks, which may involve not just two but…