Given two graphs G and H, an H-decomposition of G is a partition of the
edge set of G such that each part is either a single edge or forms a graph
isomorphic to H. Let f(n;H) be the smallest number  such that any graph
G of order n admits an H-decomposition with at most f(n;H)  parts. Pikhurko and
Sousa conjectured that f(n;H) = ex(n;H) for (H)  3 and all sufficiently
large n, where ex(n;H) denotes the maximum number of edges in a graph on n vertices not containing H as a subgraph. Their conjecture has been veried by
Ozkahya and Person for all edge-critical graphs H. In this article, the conjecture
is veried for the k-fan graph. The k-fan graph, denoted by F_k, is the graph on
2k + 1 vertices consisting of k triangles which intersect in exactly one common
vertex called the centre of the k-fan.

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Let $\Omega_n$ be a finite chain with $n$ elements $(n\in\mathbb{N})$, and let $\mathcal{POPI}_{n}$ be the semigroup of all injective orientation-preserving partial transformations of $\Omega_n$. In this paper, for any nonempty subset $Y$ of $\Omega_n$, we consider the subsemigroup $\mathcal{POPI}_{n}(Y)$ of $\mathcal{POPI}_{n}$ of all transformations with range contained in $Y$. We describe the Green's relations and study the regularity of $\mathcal{POPI}_{n}(Y)$. Moreover, we calculate the rank of $\mathcal{POPI}_{n}(Y)$ and determine when two semigroups of this type are isomorphic.

Industrial robots are increasingly integrated into manufacturing workspaces, leading to significant changes in work design and altering workers’ framing of work and technology. Even without anthropomorphic design or autonomous features, employees may treat industrial robots as more than mere tools, attributing human-like qualities to them. Yet, prior research typically considers technology either as a tool or as an occasion for altering work relationships between humans, overlooking how relationships with technology itself are crafted. Drawing on 133 interviews across multiple organizations—including robot users, robot producers, and solution providers, we show that mind perceptions (attributions of agency and experience to industrial robots) catalyze relational job crafting with robots. We identify four co-evolving practices—crafting responsibilities, crafting hierarchies, crafting collaboration, and crafting emotional connection—that help workers regain control and regulate daily stress levels, thereby linking relational crafting to both performance and well-being outcomes. Our study extends relational job crafting theory by theorizing mind perceptions as the trigger of human-robot relationality and shifts attention from agentic/anthropomorphic design of technologies to workers’ perceptions of these technologies as core drivers of human-robot-interaction and technology adoption in organizations.

In this paper we address a wireless network design problem on a railway line. Given a finite set of locations along a railway line and different types of communication antennas that can be installed at each of these locations, which locations and which type of antenna should be selected to ensure a certain level of signal coverage along the railway line while minimizing construction costs? We formulate the problem as a 0/1 linear optimization model, prove that the problem is NP-hard, and report computational experiments using real and simulated data. The computational tests showed that the model is capable of solving the problem for railway lines longer than any existing real railway lines.

High-dimensional omics data often contain more variables than observations, which can lead to overfitting and negatively impact the results of classical data analysis methods. To address the issue, supervised variable selection methods are often used, incorporating penalty terms into the model. While effective for selecting task-specific variables, this approach may not preserve the overall dataset structure for multiple downstream analyses. This study aims to evaluate unsupervised variable selection approaches and introduce a novel tool that improves data interpretability while maintaining biological information.