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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






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


Zap. Nauchn. Sem. POMI, 2016, Volume 450, Pages 62–73 (Mi znsl6337)  

Lower bounds on the number of leaves in spanning trees

D. V. Karpovab

a St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
b St. Petersburg State University, St. Petersburg, Russia

Abstract: Let $G$ be a connected graph on $n\ge2$ vertices with girth at least $g$. Let maximal chain of successively adjacent vertices of degree 2 in the graph $G$ does not exceed $k\ge1$. Denote by $u(G)$ the maximal number of leaves in a spanning tree of $G$. We prove, that $u(G)\ge\alpha_{g,k}(v(G)-k-2)+2$, where $\alpha_{g,1}=\frac{[\frac{g+1}2]}{4[\frac{g+1}2]+1}$ and $\alpha_{g,k}=\frac1{2k+2}$ for $k\ge2$. We present infinite series of examples showing that all these bounds are tight.

Key words and phrases: spanning tree, number of leaves.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.Z50.31.0030
НШ-9721.2016.1
Russian Foundation for Basic Research 14-01-00156


Full text: PDF file (213 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2018, 232:1, 36–43

Bibliographic databases:

UDC: 519.172.1
Received: 11.10.2016

Citation: D. V. Karpov, “Lower bounds on the number of leaves in spanning trees”, Combinatorics and graph theory. Part VIII, Zap. Nauchn. Sem. POMI, 450, POMI, St. Petersburg, 2016, 62–73; J. Math. Sci. (N. Y.), 232:1 (2018), 36–43

Citation in format AMSBIB
\Bibitem{Kar16}
\by D.~V.~Karpov
\paper Lower bounds on the number of leaves in spanning trees
\inbook Combinatorics and graph theory. Part~VIII
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 450
\pages 62--73
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6337}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3582953}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2018
\vol 232
\issue 1
\pages 36--43
\crossref{https://doi.org/10.1007/s10958-018-3857-2}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85047306988}


Linking options:
  • http://mi.mathnet.ru/eng/znsl6337
  • http://mi.mathnet.ru/eng/znsl/v450/p62

    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
  • Записки научных семинаров ПОМИ
    Number of views:
    This page:84
    Full text:20
    References:12

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019