Geodesic
Finding a family of simple circuits in graphs with~vertex semidegrees bounded by~$k$
Prikladnaâ diskretnaâ matematika, no. 2 (2023), pp. 85-94

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We study the algorithmic complexity of finding a family of simple circuits passing every vertice of a digraph with semidegree bounded by $k$. The problem is considered in two variants: as a search and as an optimization problem. Parametrically polynomial solvability of the problem is proved in both variants, Algorithms with complexity $O(nk^2 + n\log_{2}n)$, $O(n(k^2 + k) + n\log_{2}n)$ and $O(n)$ for various types of constraints are proposed, where $n$ is the number of digraph vertices.
Keywords: digraphs, search problems, optimization, parametrical complexity, polynomial solvability.
Mots-clés : simple circuits, P class 
@article{PDM_2023_2_a6,
     author = {A. A. Medvedev},
     title = {Finding a family of simple circuits in graphs with~vertex semidegrees bounded by~$k$},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {85--94},
     publisher = {mathdoc},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2023_2_a6/}
}
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A. A. Medvedev. Finding a family of simple circuits in graphs with~vertex semidegrees bounded by~$k$. Prikladnaâ diskretnaâ matematika, no. 2 (2023), pp. 85-94. http://geodesic.mathdoc.fr/item/PDM_2023_2_a6/