In this paper we solve a conjecture of P. Erdös by showing that if a graph Gn has n vertices and at least 100kn1+ 1 k edges, then G contains a cycle C2l of length 2l for every integer l ∈ [k, kn 1 k]. Apart from the value of the constant this result is best possible. It is obtained from a more general theorem which also yields corresponding results in the case where Gn has only cn(log n)α edges (α ≥ 1).
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics