On Erdős-Sós Conjecture for Trees of Large Size
نویسندگان
چکیده
منابع مشابه
On Erdős-Sós Conjecture for Trees of Large Size
Erdős and Sós conjectured that every graph G of average degree greater than k−1 contains every tree of size k. Several results based upon the number of vertices in G have been proved including the special cases where G has exactly k+1 vertices (Zhou), k + 2 vertices (Slater, Teo and Yap), k + 3 vertices (Woźniak) and k + 4 vertices (Tiner). We further explore this direction. Given an arbitrary ...
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Let f(n, k) be the minimum number of edges that must be removed from some complete geometric graph G on n points, so that there exists a tree on k vertices that is no longer a planar subgraph of G. In this paper we show that 1 2 n k 1 n 2 f(n, k) 2 n(n 2) k 2 . For the case when k = n, we show that 2 f(n, n) 3. For the case when k = n and G is a geometric graph on a set of points in con...
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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 کاملOn the Loebl-Komlós-Sós conjecture
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).
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/5405