Spanning Trees in Dense Graphs

Authors:
János Komlós;Gábor N. Sárkózy;Endre Szemerédi
Affiliations:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA;Computer Science Department, Worcester Polytechnic Institute, Worcester, MA 01609, USA;Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA and Hungarian Academy of Sciences, Budapest, Hungary
Venue:
Combinatorics, Probability and Computing
Year:
2001

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Abstract

In this paper we prove the following almost optimal theorem. For any δ 0, there exist constants c and n0 such that, if n ≥ n0, T is a tree of order n and maximum degree at most cn/log n, and G is a graph of order n and minimum degree at least (1/2 + δ)n, then T is a subgraph of G.