Related papers: On Hypergraph Supports

For a fixed set of positive integers $R$, we say $\mathcal{H}$ is an $R$-uniform hypergraph, or $R$-graph, if the cardinality of each edge belongs to $R$. For a graph $G=(V,E)$, a hypergraph $\mathcal{H}$ is called a Berge-$G$, denoted by…

A graph is called 1-planar if there exists its drawing in the plane such that each edge is crossed at most once. In this paper, we study 1-planar graph joins. We prove that the join $G+H$ is 1-planar if and only if the pair $[G,H]$ is…

A graph $G$ is $[a,b]$-covered if for each edge $e$ of $G$ there is an $[a,b]$-factor containing it. For $a=b=1$, an $[a,b]$-covered graph is a matching covered graph. The structural theory of matching covered graphs constitutes a…

A graph $H$ is said to be an induced minor of a graph $G$ if $H$ can be obtained from $G$ by a sequence of vertex deletions and edge contractions. Equivalently, $H$ is an induced minor of $G$ if there exists an induced minor model of $H$ in…

A matching in a hypergraph $\mathcal{H}$ is a set of pairwise disjoint hyperedges. The matching number $\nu(\mathcal{H})$ of $\mathcal{H}$ is the size of a maximum matching in $\mathcal{H}$. A subset $D$ of vertices of $\mathcal{H}$ is a…

For a fixed set ${\cal H}$ of graphs, a graph $G$ is ${\cal H}$-subgraph-free if $G$ does not contain any $H \in {\cal H}$ as a (not necessarily induced) subgraph. A recently proposed framework gives a complete classification on ${\cal…

Given a family of graphs $\mathcal{H}$, a graph $G$ is $\mathcal{H}$-free if any subset of $V(G)$ does not induce a subgraph of $G$ that is isomorphic to any graph in $\mathcal{H}$. We present sufficient and necessary conditions for a graph…

The inducibility of a graph $H$ measures the maximum number of induced copies of $H$ a large graph $G$ can have. Generalizing this notion, we study how many induced subgraphs of fixed order $k$ and size $\ell$ a large graph $G$ on $n$…

A graph $G$ contains a graph $H$ as an induced minor if $H$ can be obtained from $G$ by vertex deletions and edge contractions. The class of $H$-induced-minor-free graphs generalizes the class of $H$-minor-free graphs, but unlike…

We study the basic properties of a prime sum graph, which is a simple graph defined on $\mathbb N$ where two vertices are adjacent if and only if their sum is a prime number. Further, we investigate some specific structures that appear…

A hypergraph $\mathcal H$ is super-pancyclic if for each $A \subseteq V(\mathcal H)$ with $|A| \geq 3$, $\mathcal H$ contains a Berge cycle with base vertex set $A$. We present two natural necessary conditions for a hypergraph to be…

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…

We introduce the notion of Hypergraph Weighted Model (HWM) that generically associates a tensor network to a hypergraph and then computes a value by tensor contractions directed by its hyperedges. A series r defined on a hypergraph family…

The Surjective Homomorphism problem is to test whether a given graph G called the guest graph allows a vertex-surjective homomorphism to some other given graph H called the host graph. The bijective and injective homomorphism problems can…

This work introduces the concept of \emph{upper-critical graphs}, in a complementary way of the conventional (lower)critical graphs: an element $x$ of a graph $G$ is called \emph{critical} if $\chi(G-x)<\chi(G)$. It is said that $G$ is a…

We consider the following generalization of dominating sets: Let $G$ be a host graph and $P$ be a pattern graph $P$. A dominating $P$-pattern in $G$ is a subset $S$ of vertices in $G$ that (1) forms a dominating set in $G$ \emph{and} (2)…

Let $G$ be a finite abelian group, written additively, and $H$ a subgroup of~$G$. The \emph{subgroup sum graph} $\Gamma_{G,H}$ is the graph with vertex set $G$, in which two distinct vertices $x$ and $y$ are joined if $x+y\in…

A class $\mathcal{G}$ of graphs is called hereditary if it is closed under taking induced subgraphs. We denote by $\mathcal{G}^\mathrm{apex}$ the class of graphs $G$ that contain a vertex $v$ such that $G-v$ is in $\mathcal{G}$. We prove…

A graph $G$ with vertex set $V(G)$ and edge set $E(G)$ is said to be word-representable if there exists a word $w$ over the alphabet $V(G)$ such that, for any two distinct letters $x,y \in V(G)$, the letters $x$ and $y$ alternate in $w$ if…

Let $G$ be a graph. Adopting the terminology of Broersma et al. and \v{C}ada, respectively, we say that $G$ is 2-heavy if every induced claw ($K_{1,3}$) of $G$ contains two end-vertices each one has degree at least $|V(G)|/2$; and $G$ is…