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September 11, 2026
How to Assess Students Knowledge in the Age of AI
A researcher at HSE University has proposed a flowchart to help lecturers decide how to assess students who use artificial intelligence. It shows where the use of AI should be restricted and where it can be incorporated into the learning process. The article has been published in IT Professional.
September 9, 2026
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You cannot study spoken dialects from books. Instead, you need to go to a village, seek out its elders, and earn the trust of local residents before you can record hours of spontaneous stories. This is how Natalia Muravleva, Associate Professor at the Faculty of Humanities, conducts her research. Her internship in Serbia continued her long-standing study of dialects spoken by Macedonian settlers. In this interview, she discusses how diaspora cultural centres help researchers reach informants, why native speakers need to be interviewed only in their own language (otherwise, as she puts it, they may 'break'), and how a single field season helped her finalise her monograph. She also shares warm memories of autumn in Belgrade and of colleagues with whom grammar can be discussed in three languages at once.
September 9, 2026
Scientists Train Neural Network to Generate Process Plans from 3D Models
Researchers at the HSE FCS AI and Digital Science Institute have developed CAD2TechSpec, a framework that converts 3D models of mechanical parts into machining process plans—step-by-step instructions for machine tools. The solution aims to reduce the time required for the design and preparation of technical process documentation in mechanical engineering, aircraft manufacturing, and other high-tech industries. The study findings have been published in PeerJ Computer Science.

 

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On the number of independent and k-dominating sets in graphs with average vertex degree at most k

Sbornik Mathematics. 2023. Vol. 214. No. 11. P. 1627–1650.
D. S. Taletskii

The following conjecture is formulated: if the average vertex degree in a graph is not greater than a positive integer k⩾1, then the number of k-dominating sets in this graph does not exceed the number of its independent sets, and these numbers are equal to each other if and only if the graph is k-regular. This conjecture is proved for k∈{1,2}.

Research target: Mathematics
Language: English
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Keywords: enumerative combinatoricsdominating setindependent setk-dominating set
Publication based on the results of:
Research on graph and network structures and its applications (2023)
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