相关论文: New constructions for the $n$-queens problem

We study the domination number $\gamma(Q_n^3)$ of the three-dimensional $n \times n \times n$ queen graph. The main result is a stratified theorem computing, for each position type -- corner, edge, face, or interior -- the number of…

A king in a directed graph is a node from which each node in the graph can be reached via paths of length at most two. There is a broad literature on tournaments (completely oriented digraphs), and it has been known for more than half a…

Let $G=(V,E)$ be a graph. A subset $D\subseteq V$ is a dominating set if every vertex not in $D$ is adjacent to a vertex in $D$. The domination number of $G$, denoted by $\gamma(G)$, is the smallest cardinality of a dominating set of $G$.…

The metric dimension is quite a well-studied graph parameter. Recently, the adjacency dimension and the local metric dimension have been introduced and studied. In this paper, we give a general formula for the local metric dimension of the…

We present the new combinatorial class of product-coproduct prographs which are planar assemblies of two types of operators: products having two inputs and a single output and coproducts having a single input and two outputs. We show that…

In this paper we provide an explicit construction of a $distinctive$ multiple Dirichlet series associated to products of quadratic Dirichlet L-series, which we believe should be tightly connected to a generalized metaplectic Whittaker…

We study a class of Legendrian surfaces in contact five-folds by encoding their wavefronts via planar combinatorial structures. We refer to these surfaces as Legendrian weaves, and to the combinatorial objects as N-graphs. First, we develop…

We study the problem of conjunctive query evaluation relative to a class of queries; this problem is formulated here as the relational homomorphism problem relative to a class of structures A, wherein each instance must be a pair of…

A prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given the number of…

A graph is an instrument which is extensively utilized to model various problems in different fields. Up to date, many graphs have been developed to represent algebraic structures, particularly rings in order to study their properties. In…

A prime labeling on a graph of order $m$ is an assignment of $\{ 1, 2, \ldots, m \}$ to the vertices of the graph such that each pair of adjacent vertices has coprime labels. The ladder of order $2n$ is the $2 \times n$ grid graph graph…

Let $G$ be a connected complex reductive algebraic group with Lie algebra $\mathfrak{g}$. The Lusztig--Vogan bijection relates two bases for the bounded derived category of $G$-equivariant coherent sheaves on the nilpotent cone…

For a Lie-Rinehart algebra (A,L), generators for the Gerstenhaber algebra \Lambda_A L correspond bijectively to right (A,L)-connections on A in such a way that B-V structures correspond to right (A,L)-module structures on A. When L is…

A well-known chessboard problem is that of placing eight queens on the chessboard so that no two queens are able to attack each other. (Recall that a queen can attack anything on the same row, column, or diagonal as itself.) This problem is…

In hypergraph theory, determining a characterization of the degree sequence $d=(d_1,d_2,\ldots,d_n)$ where $d_1\ge d_2\ge\ldots,d_n$ are positive integers, of an $h$-uniform simple hypergraph $\cal H$, and deciding the complexity status of…

An out-branching $B^+_u$ (in-branching $B^-_u$) in a digraph $D$ is a connected spanning subdigraph of $D$ in which every vertex except the vertex $u$, called the root, has in-degree (out-degree) one. A {\bf good $\mathbf{(u,v)}$-pair} in…

A graph $G$ covers a graph $H$ if there exists a locally bijective homomorphism from $G$ to $H$. We deal with regular covers where this homomorphism is prescribed by the action of a semiregular subgroup of $\textrm{Aut}(G)$. We study…

Balliu et al. (DISC 2020) classified the hardness of solving binary labeling problems with distributed graph algorithms; in these problems the task is to select a subset of edges in a $2$-colored tree in which white nodes of degree $d$ and…

Given a matrix M of size n, a digraph D on n vertices is said to be the digraph of M, when M_{ij} is different from 0 if and only if (v_{i},v_{j}) is an arc of D. We give a necessary condition, called strong quadrangularity, for a digraph…

For a positive integer \( k \), let \( [k] = \{1, 2, \ldots, k\} \). Let \( h \) be a non-negative integer, and let \( n \) be a multiple of \( h + 1 \). Define \( H \) as the disjoint union of \( n/(h+1) \) cliques (each of size \( h + 1…