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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

An approximate version of the Loebl-Komlos-Sos conjecture

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Author(s):
Piguet, Diana [1] ; Jakobine Stein, Maya [2]
Total Authors: 2
Affiliation:
[1] Univ Birmingham, Sch Math, Birmingham B15 2TT, W Midlands - England
[2] Univ Chile, Santiago - Chile
Total Affiliations: 2
Document type: Journal article
Source: JOURNAL OF COMBINATORIAL THEORY SERIES B; v. 102, n. 1, p. 102-125, JAN 2012.
Web of Science Citations: 9
Abstract

Loebl, Komlos, and Sos conjectured that if at least half of the vertices of a graph G have degree at least some k is an element of N. then every tree with at most k edges is a subgraph of G. Our main result is an approximate version of this conjecture for large enough n = vertical bar V(G)vertical bar, assumed that n = O (k). Our result implies an asymptotic bound for the Ramsey number of trees. We prove that r(T(k), T(m)) <= k + m + o(k + m), as k + m -> infinity. (C) 2011 Elsevier Inc. All rights reserved. (AU)