The inflation $G_{I}$ of a graph $G$ with $n(G)$ vertices and $m(G)$ edges is obtained from $G$ by replacing every vertex of degree $d$ of $G$ by a clique, which is isomorph to the complete graph $K_{d}$, and each edge $(x_{i},x_{j})$ of $G$ is replaced by an edge $(u,v)$ in such a way that $uin X_{i}$, $vin X_{j}$, and two different edges of $G$ are replaced by non-adjacent edges of $G_{I}$. T...

Let K be a field and let $$S=K[x_1,\ldots ,x_n]$$ standard polynomial ring over K. We characterize the extremal Betti numbers, values as well positions, of t-spread strongly stable ideal S. Our approach is constructive. Indeed, given some positive integers $$a_1,\dots ,a_r$$ pairs $$(k_1,\ell _1),\ldots ,(k_r,\ell _r)$$ , we are able to determine under which conditions there exists I S with $$\...

Abstract Motivated by analogous questions in the setting of Steiner triple systems and Latin squares, Nenadov, Sudakov Wagner [Completion deficiency problems, Journal Combinatorial Theory Series B, 2020] recently introduced notion graph . Given a global spanning property $\mathcal P$ $G$ , $\text{def}(G)$ with respect to is smallest non-negative integer t such that join $G*K_t$ has In particula...

Abstract We prove that, for every graph F with at least one edge, there is a constant $$c_F$$ c F such that are graphs of arbitrarily large chromatic number and the same clique as in which -free induced subgraph has most . This generalises recent theorems Briański, Davi...

We consider the vertex cover problem with multiple coverage constraints in hypergraphs. In this problem, we are given a hypergraph \(G=(V,E)\) maximum edge size f, cost function \(w: V\rightarrow {\mathbb {Z}}^+\), and subsets \(P_1,P_2,\ldots ,P_r\) of E along covering requirements \(k_1,k_2,\ldots ,k_r\) for each subset. The objective is to find minimum subset S V such that, \(P_i\), at least...

A recent 2D spinFET concept proposes to switch electrostatically between two separate sublayers with strong and opposite intrinsic Rashba effects. This exploits the spin-layer locking mechanism present in centrosymmetric materials local dipole fields, where a weak electric field can easily manipulate just one of spin channels. Here, we propose novel monolayer material within this family, luteti...

Given integers r ⩾ 2 $r\geqslant 2$ and n , t 1 $n,t\geqslant 1$ we call families F ⋯ ⊆ P ( [ ] ) $\mathcal {F}_1,\dots ,\mathcal {F}_r\subseteq \mathcal {P}([n])$ $r$ -cross $t$ -intersecting if for all i ∈ $F_i\in {F}_i$ $i\in [r]$ have | ∩ $\vert \bigcap _{i\in [r]}F_i\vert \geqslant t$ . We obtain a strong generalisation of the classic Hilton–Milner theorem on cross-intersecting families. I...

We introduce an exact analytical solution of the homogeneous space-fractional Helmholtz equation in cylindrical coordinates. This solution, called vector Space-Fractional Bessel Beam (SFBB), has been established from Lorenz' gauge condition and Hertz transformations. perform scalar wave analysis focusing on electromagnetics applications, especially cases where dimensions beam are comparable to ...

Abstract We consider the problem of covering multiple submodular constraints. Given a finite ground set N , weight function $$w: \rightarrow \mathbb {R}_+$$ w : N → R + r monotone...