Geodesic
Hypergraph edge representations with~the~use~of~homological paths
Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 3, pp. 81-95.

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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. 
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M. N. Vyalyi; V. E. Karpov. Hypergraph edge representations with~the~use~of~homological paths. Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 3, pp. 81-95. http://geodesic.mathdoc.fr/item/DA_2023_30_3_a3/

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