Author:
Dang Dinh Hanh Department of Mathematics, Hanoi Architectural University, km10, NguyenTrai str., Hanoi, Vietnam

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A leaf of a tree is a vertex of degree one and a branch vertex of a tree is a vertex of degree at least three. In this paper, we show a degree condition for a claw-free graph to have spanning trees with at most five branch vertices and leaves in total. Moreover, the degree sum condition is best possible.

  • [1]

    Y. Chen, P. H. Ha and D. D. Hanh. Spanning trees with at most 4 leaves in K1,5-free graphs. Discrete Math, 342:2342-2349, 2019.

  • [2]

    R. Gould, W. Shull. On spanning trees with few branch vertices. Discrete Math, 343:111581, 2020.

  • [3]

    M. Kano, A. Kyaw, H. Matsuda, K. Ozeki, A. Saito and T. Yamashita. Spanning trees with a bounded number of leaves in a claw-free graph. Ars Combinatoria, 103:137-154, 2012.

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  • [4]

    A. Kyaw. Spanning trees with at most k leaves in K1,4-free graphs. Discrete Math, 311:21352142, 2011.

  • [5]

    H. Matsuda, K. Ozeki and T. Yamashita. Spanning trees with a bounded number of branch vertices in a claw-free graph. Graphs and Combinatorics, 30:429-437, 2014.

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    • Export Citation
  • [6]

    S. Maezawa, R. Matsubara and H. Matsuda. Degree conditions for graphs to have spanning trees with few branch vertices and leaves. Graphs and Combinatorics, 35:231-238, 2019.

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    • Export Citation
  • [7]

    ZhG. Nikoghosyan. Spanning trees with few branch and end vertices. Math. Probl. Comput. Sci, 46:15-28, 2016.

  • [8]

    A. Saito and K. Sano. Spanning trees homeomorphic to a small tree. Discrete. Math, 339:677681, 2016.

  • [9]

    P. Wang and J. Cai. Spanning trees with at most 4 leaves in k1,5-free graphs. Discrete Math, 342:1546-1552, 2019.

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Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

Editorial Board

  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation
1966
Volumes
per Year
1
Issues
per Year
4
Founder Magyar Tudományos Akadémia  
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Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
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Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)