Loebl-Komlós-Sós Conjecture: Dense case
نویسندگان
چکیده
We prove a version of the Loebl-Komlós-Sós Conjecture for dense graphs. For any q > 0 there exists a number n0 ∈ N such that for any n > n0 and k > qn the following holds: if G be a graph of order n with at least n/2 vertices of degree at least k, then any tree of order k +1 is a subgraph of G.
منابع مشابه
ar X iv : 0 80 5 . 48 34 v 3 [ m at h . C O ] 6 S ep 2 00 8 Loebl - Komlós - Sós Conjecture : dense case
We prove a version of the Loebl-Komlós-Sós Conjecture for dense graphs. For any q > 0 there exists a number n0 ∈ N such that for any n > n0 and k > qn the following holds: if G be a graph of order n with at least n/2 vertices of degree at least k, then any tree of order k +1 is a subgraph of G.
متن کاملProof of the Loebl-Komlós-Sós conjecture for large, dense graphs
The Loebl–Komlós–Sós conjecture states that for any integers k and n, if a graph G on n vertices has at least n/2 vertices of degree at least k, then G contains as subgraphs all trees on k + 1 vertices. We prove this conjecture in the case when k is linear in n, and n is sufficiently large. © 2009 Elsevier B.V. All rights reserved.
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The Loebl-Komlós-Sós conjecture says that any graph G on n vertices with at least half of vertices of degree at least k contains each tree of size k. We prove that the conjecture is true for paths as well as for large values of k (k ≥ n− 3).
متن کاملThe Loebl-Komlós-Sós Conjecture for Trees of Diameter 5 and for Certain Caterpillars
Loebl, Komlós, and Sós conjectured that if at least half the vertices of a graph G have degree at least some k ∈ N, then every tree with at most k edges is a subgraph of G. We prove the conjecture for all trees of diameter at most 5 and for a class of caterpillars. Our result implies a bound on the Ramsey number r(T, T ) of trees T, T ′ from the above classes.
متن کاملAn approximate version of the Loebl-Komlós-Sós conjecture
Loebl, Komlós, and Sós conjectured that if at least half of the vertices of a graph G have degree at least some k ∈ 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 = |V (G)|, assumed that n = O(k). Our result implies an asymptotic bound for the Ramsey number of trees. We prove that r(Tk, Tm) ≤ k + m + o(...
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ورودعنوان ژورنال:
- Electronic Notes in Discrete Mathematics
دوره 34 شماره
صفحات -
تاریخ انتشار 2009