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The Erdős-Sós Conjecture for Graphs Whose Complements Contain No C 4

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Abstract

Erdős and Sós conjectured in 1963 (see [1], Problem 12 in 247) that every graph G on n vertices with size \( e{\left( G \right)} > \frac{1} {2}n{\left( {k - 1} \right)} \) contains every tree T of size k. In this paper, we prove the conjecture for graphs whose complements contain no cycles of length 4.

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Authors and Affiliations

  1. Department of Applied Mathematics, College of Information Science and Technology, Hainan University, Haikou, 570228, China

    Jian-hua Yin

  2. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China

    Jiong-sheng Li

Authors
  1. Jian-hua Yin
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  2. Jiong-sheng Li
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Corresponding author

Correspondence to Jian-hua Yin.

Additional information

Supported by the National Natural Science Foundation of China (No.19971086) and the Doctoral Foundation of Hainan University.

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Yin, Jh., Li, Js. The Erdős-Sós Conjecture for Graphs Whose Complements Contain No C 4 . Acta Mathematicae Applicatae Sinica, English Series 20, 397–400 (2004). https://doi.org/10.1007/s10255-004-0178-7

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  • DOI: https://doi.org/10.1007/s10255-004-0178-7

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