Related papers: Hypertrees and their host trees: a survey
Tree representations of (sets of) symmetric binary relations, or equivalently edge-colored undirected graphs, are of central interest, e.g.\ in phylogenomics. In this context symbolic ultrametrics play a crucial role. Symbolic ultrametrics…
We consider homomorphisms of signed graphs from a computational perspective. In particular, we study the list homomorphism problem seeking a homomorphism of an input signed graph $(G,\sigma)$, equipped with lists $L(v) \subseteq V(H), v \in…
The class ${\cal L}_k$ of $k$-leaf powers consists of graphs $G=(V,E)$ that have a $k$-leaf root, that is, a tree $T$ with leaf set $V$, where $xy \in E$, if and only if the $T$-distance between $x$ and $y$ is at most $k$. Structure and…
As set systems, hypergraphs are omnipresent and have various representations ranging from Euler and Venn diagrams to contact representations. In a geometric representation of a hypergraph $H=(V,E)$, each vertex $v\in V$ is associated with a…
Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applicability in various network mining problems, including…
Arboreal networks are a generalization of rooted trees, defined by keeping the tree-like structure, but dropping the requirement for a single root. Just as the class of cographs is precisely the class of undirected graphs that can be…
A hypergraph is a data structure composed of nodes and hyperedges, where each hyperedge is an any-sized subset of nodes. Due to the flexibility in hyperedge size, hypergraphs represent group interactions (e.g., co-authorship by more than…
Let $G$ be a graph on $n\geq 3$ vertices. A graph $G$ is almost distance-hereditary if each connected induced subgraph $H$ of $G$ has the property $d_{H}(x,y)\leq d_{G}(x,y)+1$ for any pair of vertices $x,y\in V(H)$. A graph $G$ is called…
Hypergraphs are generalizations of simple graphs that allow for the representation of complex group interactions beyond pairwise relationships. Clustering coefficients quantify local link density in networks and have been widely studied for…
We define an algebraic setup of homology for hypergraphs, which defaults to simplicial homology in the case of graphs, and study its basic properties. As part of our study we define algebraic spanning trees of hypergraphs, along with…
We introduce a new graph parameter, the hydra number, arising from the minimization problem for Horn formulas in propositional logic. The hydra number of a graph $G=(V,E)$ is the minimal number of hyperarcs of the form $u,v\rightarrow w$…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
This paper revisits the notion of a spanning hypertree of a hypermap introduced by one of its authors and shows that it allows to shed new light on a very diverse set of recent results. The tour of a map along one of its spanning trees used…
Hovey introduced $A$-cordial labelings as a generalization of cordial and harmonious labelings \cite{Hovey}. If $A$ is an Abelian group, then a labeling $f \colon V (G) \rightarrow A$ of the vertices of some graph $G$ induces an edge…
The number of spanning trees in a graph $G$ is the total number of distinct spanning subgraphs of $G$ that are trees. In this paper we characterize the unique graph with a prescribed vertex (resp. edge) connectivity, minimum degree and…
A circular-arc hypergraph $H$ is a hypergraph admitting an arc ordering, that is, a circular ordering of the vertex set $V(H)$ such that every hyperedge is an arc of consecutive vertices. An arc ordering is tight if, for any two hyperedges…
A graph $G$ is said to be Hamiltonian if it contains a spanning cycle. In this work, we investigate the Hamiltonian completeness of certain classes of caterpillar graphs, which are trees with a central path to which all other vertices are…
The Spanning Tree Congestion (STC) problem is the following NP-hard problem: given a graph $G$, construct a spanning tree $T$ of $G$ minimizing its maximum edge congestion where the congestion of an edge $e\in T$ is the number of edges $uv$…
We investigate the product structure of hereditary graph classes admitting strongly sublinear separators. We characterise such classes as subgraphs of the strong product of a star and a complete graph of strongly sublinear size. In a more…
Lorea [11] and later Frank et al. [8] generalized graphic matroids to hypergraphic matroids. In [8], the authors introduced hypertrees as a generalization of spanning trees and proved a form of the theorem of Tutte [18] and Nash-Williams…