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author:

Fan, Genghua (Fan, Genghua.) [1] (Scholars:范更华) | Sun, Lingli (Sun, Lingli.) [2]

Indexed by:

EI Scopus SCIE

Abstract:

A classical result on extremal graph theory is the Erdos-Gallai theorem: if a graph on n vertices has more than (k-1)n/2 edges, then it contains a path of k edges. Motivated by the result, Erdos and Sos conjectured that under the same condition, the graph should contain every tree of k edges. A spider is a rooted tree in which each vertex has degree one or two, except for the root. A leg of a spider is a path from the root to a vertex of degree one. Thus, a path is a spider of 1 or 2 legs. From the motivation, it is natural to consider spiders of 3 legs. In this paper, we prove that if a graph on n vertices has more than (k-1)n/2 edges, then it contains every k-edge spider of 3 legs, and also, every k-edge spider with no leg of length more than 4, which strengthens. a result of Wozniak on spiders of diameter at most 4. (C) 2007 Elsevier B.V. All rights reserved.

Keyword:

Erdos-Sos conjecture spiders trees

Community:

  • [ 1 ] [Fan, Genghua]Fuzhou Univ, Dept Math, Fujian 350002, Peoples R China
  • [ 2 ] [Sun, Lingli]Huazhong Agr Univ, Coll Basic Sci, Dept Maths & Informat Sci, Wuhan 430070, Peoples R China

Reprint 's Address:

  • 范更华

    [Fan, Genghua]Fuzhou Univ, Dept Math, Fujian 350002, Peoples R China

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Source :

DISCRETE MATHEMATICS

ISSN: 0012-365X

Year: 2007

Issue: 23

Volume: 307

Page: 3055-3062

0 . 3 7 7

JCR@2007

0 . 7 0 0

JCR@2023

ESI Discipline: MATHEMATICS;

JCR Journal Grade:3

Cited Count:

WoS CC Cited Count: 15

SCOPUS Cited Count: 23

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 4

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