Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 59: Issue 1
Degree Conditions for Claw-Free Graphs to Have Spanning Trees with at Most Five Branch Vertices and Leaves in Total
Author:
Dang Dinh Hanh Department of Mathematics, Hanoi Architectural University, km10, NguyenTrai str., Hanoi, Vietnam

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Pages:
58–66
Online Publication Date:
01 Apr 2022
Publication Date:
01 Apr 2022
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2022.01521
Keywords:
spanning tree; branch vertices; leaves; claw-free
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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.

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    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.

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

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

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    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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    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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  • [7]

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

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

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    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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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

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

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Gábor SÁGI (Rényi Institute of Mathematics)

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  • 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  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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