Related papers: Hypergraph Characterization of Fusion Rings

A matching of graph $G$ is maximal if it cannot be expanded by adding any edge to create a larger matching. In this paper, for a hexagonal ring $H$ with $n$ hexagons, we show that the number of maximal matchings of $H$ equals to the trace…

In this paper, we investigate the holographic descriptions of two kinds of black rings, the neutral doubly rotating black ring and the dipole charged black ring. For generic nonextremal black rings, the information of holographic CFT duals,…

A formula for computing the metric dimension of a simple graph, having no singleton twin, is given. A sufficient condition for a simple graph to have the exchange property, for resolving sets, is found. Some families of power graphs of…

In the homomorphism order of digraphs, a duality pair is an ordered pair of digraphs $(G,H)$ such that for any digraph, $D$, $G\to D$ if and only if $D\not\to H$. The directed path on $k+1$ vertices together with the transitive tournament…

A graph is $H$-free if it does not contain $H$ as a subgraph. The diamond graph is the graph obtained from $K_4$ by deleting one edge. We prove that if $G$ is a connected graph with order $n\geq 10$, then there exists a subset $S\subseteq…

We present an overview of the close analogies between the character rings of finite groups and the fusion rings of rational conformal models, which follow from general principles related to orbifold deconstruction.

A fusion category of rank $4$ has either four self-dual objects or exactly two self-dual objects. We study fusion categories of rank $4$ with exactly two self-dual objects, giving nearly a complete classification of those based ring that…

For a digraph $D$ of order $n$ and an integer $1 \leq k \leq n-1$, the $k$-token digraph of $D$ is the graph whose vertices are all $k$-subsets of vertices of $D$ and, given two such $k$-subsets $A$ and $B$, $(A,B)$ is an arc in the…

The independence number $\alpha(H)$ of a hypergraph $H$ is the maximum cardinality of a set of vertices of $H$ that does not contain an edge of $H$. Generalizing Shearer's classical lower bound on the independence number of triangle-free…

We study unit groups of rings of the form $\mathbb{F}_2[x,y]/(y^2 + gy + h)$, for $g, h \in \mathbb{F}_2[x]$ -- in particular, the question of (non)triviality of such unit groups. Up to automorphisms of $\mathbb{F}_2[x,y]$ we classify such…

Let $S, K$ be two subrings of a finite ring $R$. Then the generalized non-commuting graph of subrings $S, K$ of $R$, denoted by $\Gamma_{S, K}$, is a simple graph whose vertex set is $(S \cup K) \setminus (C_K(S) \cup C_S(K))$ and two…

There is a natural one-to-one correspondence between squarefree monomial ideals and finite simple hypergraphs via the cover ideal construction. Let H be a finite simple hypergraph, and let J = J(H) be its cover ideal in a polynomial ring R.…

Motivated to find the answers to some of the questions that have occurred in recent papers dealing with Hamiltonian cycles (abbreviated HCs) in some special classes of grid graphs we started the investigation of spanning unions of cycles,…

Simple drawings are drawings of graphs in which any two edges intersect at most once (either at a common endpoint or a proper crossing), and no edge intersects itself. We analyze several characteristics of simple drawings of complete…

For a graph $G$ and a set of graphs $\mathcal{H}$, we say that $G$ is {\em $\mathcal{H}$-free} if no induced subgraph of $G$ is isomorphic to a member of $\mathcal{H}$. Given an integer $P>0$, a graph $G$, and a set of graphs $\mathcal{F}$,…

Ozkan et al. conjectured that any packing of $n$ spheres with generic radii will be stress-free, and hence will have at most $3n-6$ contacts. In this paper we prove that this conjecture is true for any sphere packing with contact graph of…

A \textbf{strong arc decomposition} of a (multi-)digraph $D(V, A)$ is a partition of its arc set $A$ into two disjoint arc sets $A_1$ and $A_2$ such that both of the spanning subdigraphs $D(V, A_1)$ and $D(V, A_2)$ are strong. In this…

Let p be a singular point of a variety. Consider a resolution where the preimage of p is a simple normal crossing divisor E. The combinatorial structure of E is described by a cell complex D(E), called the dual graph or dual complex of E.…

We show that the vertices and edges of a $d$-dimensional grid graph $G=(V,E)$ ($d\geqslant 2$) can be labeled with the integers from $\{1,\ldots,\lvert V\rvert\}$ and $\{1,\ldots,\lvert E\rvert\}$, respectively, in such a way that for every…

We define a new combinatorial object, which we call a labeled hypergraph, uniquely associated to any square-free monomial ideal. We prove several upper bounds on the regularity of a square-free monomial ideal in terms of simple…