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Model. Anal. Inform. Sist., 2015, Volume 22, Number 4, Pages 453–463 (Mi mais452)  

This article is cited in 2 scientific papers (total in 2 papers)

1-Skeletons of the spanning tree problems with additional constraints

V. A. Bondarenko, A. V. Nikolaev, D. A. Shovgenov

P.G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia

Abstract: In this paper, we study polyhedral properties of two spanning tree problems with additional constraints. In the first problem, it is required to find a tree with a minimum sum of edge weights among all spanning trees with the number of leaves less than or equal to a given value. In the second problem, an additional constraint is the assumption that the degree of all nodes of the spanning tree does not exceed a given value. The recognition versions of both problems are NP-complete. We consider polytopes of these problems and their 1-skeletons. We prove that in both cases it is a NP-complete problem to determine whether the vertices of 1-skeleton are adjacent. Although it is possible to obtain a superpolynomial lower bounds on the clique numbers of these graphs. These values characterize the time complexity in a broad class of algorithms based on linear comparisons. The results indicate a fundamental difference between combinatorial and geometric properties of the considered problems from the classical minimum spanning tree problem.

Keywords: spanning tree, 1-skeleton, clique number, NP-complete problem, hamiltonian chain.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00333
Ministry of Education and Science of the Russian Federation МК-5400.2015.13


DOI: https://doi.org/10.18255/1818-1015-2015-4-453-463

Full text: PDF file (192 kB)
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Bibliographic databases:

UDC: 519.16+514.172.45
Received: 30.07.2015

Citation: V. A. Bondarenko, A. V. Nikolaev, D. A. Shovgenov, “1-Skeletons of the spanning tree problems with additional constraints”, Model. Anal. Inform. Sist., 22:4 (2015), 453–463

Citation in format AMSBIB
\Bibitem{BonNikSho15}
\by V.~A.~Bondarenko, A.~V.~Nikolaev, D.~A.~Shovgenov
\paper 1-Skeletons of the spanning tree problems with additional constraints
\jour Model. Anal. Inform. Sist.
\yr 2015
\vol 22
\issue 4
\pages 453--463
\mathnet{http://mi.mathnet.ru/mais452}
\crossref{https://doi.org/10.18255/1818-1015-2015-4-453-463}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3418466}
\elib{http://elibrary.ru/item.asp?id=24273047}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Bondarenko, A. V. Nikolaev, D. A. Shovgenov, “Poliedralnye kharakteristiki zadach o sbalansirovannom i nesbalansirovannom dvudolnykh podgrafakh”, Model. i analiz inform. sistem, 24:2 (2017), 141–154  mathnet  crossref  elib
    2. V. A. Bondarenko, A. V. Nikolaev, “On the skeleton of the polytope of pyramidal tours”, J. Appl. Industr. Math., 12:1 (2018), 9–18  mathnet  crossref  crossref  elib
  • Моделирование и анализ информационных систем
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