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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 406, Pages 67–94 (Mi znsl5290)  
This article is cited in 3 scientific papers (total in 3 papers)

Spanning trees with many leaves: lower bounds in terms of number of vertices of degree 1, 3 and at least 4

D. V. Karpov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (343 kB) Citations (3)
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Abstract: We prove that every connected graph with $s$ vertices of degree 1 and 3 and $t$ vertices of degree at least 4 has a spanning tree with at least $\frac13t+\frac14s+\frac32$ leaves. We present an infinite series of graphs showing that our bound is tight.
Key words and phrases: spanning tree, leaves, number of leaves.
Received: 23.05.2012
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 196, Issue 6, Pages 768–783
DOI: https://doi.org/10.1007/s10958-014-1692-7
Bibliographic databases:
Document Type: Article
UDC: 519.172.1
Language: Russian
Citation: D. V. Karpov, “Spanning trees with many leaves: lower bounds in terms of number of vertices of degree 1, 3 and at least 4”, Combinatorics and graph theory. Part V, Zap. Nauchn. Sem. POMI, 406, POMI, St. Petersburg, 2012, 67–94; J. Math. Sci. (N. Y.), 196:6 (2014), 768–783
Citation in format AMSBIB
\Bibitem{Kar12}
\by D.~V.~Karpov
\paper Spanning trees with many leaves: lower bounds in terms of number of vertices of degree~1, 3 and at least~4
\inbook Combinatorics and graph theory. Part~V
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 406
\pages 67--94
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5290}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3032176}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 196
\issue 6
\pages 768--783
\crossref{https://doi.org/10.1007/s10958-014-1692-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84914098124}
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  • https://www.mathnet.ru/eng/znsl/v406/p67
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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