RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Diskretn. Anal. Issled. Oper.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Diskretn. Anal. Issled. Oper., 2018, Volume 25, Issue 2, Pages 101–123 (Mi da898)  

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

On trees of bounded degree with maximal number of greatest independent sets

D. S. Taletskiia, D. S. Malyshevba

a Lobachevsky Nizhny Novgorod State University, 23 Gagarina Ave., 603950 Nizhny Novgorod, Russia
b National Research University Higher School of Economics, 25/12 Bolshaya Pechyorskaya St., 603155 Nizhny Novgorod, Russia

Abstract: Given $n$ and $d$, we describe the structure of trees with the maximal possible number of greatest independent sets in the class of $n$-vertex trees of vertex degree at most $d$. We show that the extremal tree is unique for all even $n$ but uniqueness may fail for odd $n$; moreover, for $d=3$ and every odd $n\geq7$, there are exactly $\lceil(n-3)/4\rceil+1$ extremal trees. In the paper, the problem of searching for extremal $(n,d)$-trees is also considered for the $2$-caterpillars; i.e., the trees in which every vertex lies at distance at most $2$ from some simple path. Given $n$ and $d\in\{3,4\}$, we completely reveal all extremal $2$-caterpillars on $n$ vertices each of which has degree at most $d$. Illustr. 9, bibliogr. 10.

Keywords: extremal combinatorics, tree, greatest independent set.

Funding Agency Grant Number
Russian Science Foundation 17-11-01336
Russian Foundation for Basic Research 16-31-60008-мол-а-дк
Ministry of Education and Science of the Russian Federation


DOI: https://doi.org/10.17377/daio.2018.25.591

Full text: PDF file (446 kB)
References: PDF file   HTML file

English version:
Journal of Applied and Industrial Mathematics, 2018, 12:2, 369–381

UDC: 519.17
Received: 29.09.2017

Citation: D. S. Taletskii, D. S. Malyshev, “On trees of bounded degree with maximal number of greatest independent sets”, Diskretn. Anal. Issled. Oper., 25:2 (2018), 101–123; J. Appl. Industr. Math., 12:2 (2018), 369–381

Citation in format AMSBIB
\Bibitem{TalMal18}
\by D.~S.~Taletskii, D.~S.~Malyshev
\paper On trees of bounded degree with maximal number of greatest independent sets
\jour Diskretn. Anal. Issled. Oper.
\yr 2018
\vol 25
\issue 2
\pages 101--123
\mathnet{http://mi.mathnet.ru/da898}
\crossref{https://doi.org/10.17377/daio.2018.25.591}
\elib{https://elibrary.ru/item.asp?id=34875799}
\transl
\jour J. Appl. Industr. Math.
\yr 2018
\vol 12
\issue 2
\pages 369--381
\crossref{https://doi.org/10.1134/S1990478918020175}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85047827898}


Linking options:
  • http://mi.mathnet.ru/eng/da898
  • http://mi.mathnet.ru/eng/da/v25/i2/p101

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. D. S. Taletskii, D. S. Malyshev, “Derevya s zadannym chislom listev i maksimalno vozmozhnym kolichestvom naibolshikh nezavisimykh mnozhestv”, Diskret. matem., 32:2 (2020), 71–84  mathnet  crossref  mathscinet
    2. N. A. Kuzmin, “O derevyakh radiusa 2 s maksimalnym kolichestvom parosochetanii”, Zhurnal SVMO, 22:2 (2020), 177–187  mathnet  crossref
  • Дискретный анализ и исследование операций
    Number of views:
    This page:121
    Full text:15
    References:10
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021