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Diskretnyi Analiz i Issledovanie Operatsii, 2023, Volume 30, Issue 3, Pages 81–95
DOI: https://doi.org/10.33048/daio.2023.30.757 (Mi da1328) 		 
Hypergraph edge representations with the use of homological paths

M. N. Vyalyiabc, V. E. Karpova

a Moscow Institute of Physics and Technology, 9 Institutskii Lane, 141701 Dolgoprudnyi, Russia
b Federal Research Center “Computer Science and Control” RAS 42 Vavilov Street, 119333 Moscow, Russia
c HSE University, 11 Pokrovskii Boulevard, 109028 Moscow, Russia
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DOI: https://doi.org/10.33048/daio.2023.30.757
Abstract: We consider a problem of realization of hypergraphs on graphs provided each hyperedge is realized by a subgraph in which exactly two vertices have odd degree. This problem is related to Cycle Double Cover conjecture. We prove that checking the existence of realization is computationally hard. The hardness is proved in various settings: for realizations on all graphs, on simple graphs, and on graphs from several restricted classes. Bibliogr. 11.
Keywords: hypergraph, cycle cover, Eulerian graph, NP-completeness.
Funding agency Grant number
HSE Basic Research Program 0063--2019--0003
The work of the first author is supported by the HSE University Program for Basic Research and carried out within the framework of the state assignment of FRC CSC RAS (Project 0063–2019–0003).
Received: 21.11.2022
Revised: 27.02.2023
Accepted: 03.03.2023
Document Type: Article
UDC: 519.171
Language: Russian
Citation: M. N. Vyalyi, V. E. Karpov, “Hypergraph edge representations with the use of homological paths”, Diskretn. Anal. Issled. Oper., 30:3 (2023), 81–95
Citation in format AMSBIB
\Bibitem{VyaKar23}
\by M.~N.~Vyalyi, V.~E.~Karpov
\paper Hypergraph edge representations with~the~use~of~homological paths
\jour Diskretn. Anal. Issled. Oper.
\yr 2023
\vol 30
\issue 3
\pages 81--95
\mathnet{http://mi.mathnet.ru/da1328}
\crossref{https://doi.org/10.33048/daio.2023.30.757}
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    		Дискретный анализ и исследование операций
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