Abstract
In this paper we consider graphs which have no k vertex-disjoint cycles. For given integers k, α let f (k, α) be the maximum order of a graph G with independence number α (G) ≤ α, which has no k vertex-disjoint cycles. We prove that f (k, α) = 3 k + 2 α - 3 if 1 ≤ α ≤ 5 or 1 ≤ k ≤ 2, and f (k, α) ≥ 3 k + 2 α - 3 in general. We also prove the following results: (1) there exists a constant cα (depending only on α) such that f (k, α) ≤ 3 k + cα, (2) there exists a constant tk (depending only on k) such that f (k, α) ≤ 2 α + tk, and (3) there exists no absolute constant c such that f (k, α) ≤ c (k + α).
Original language | English |
---|---|
Pages (from-to) | 1493-1498 |
Number of pages | 6 |
Journal | Discrete Mathematics |
Volume | 307 |
Issue number | 11-12 |
DOIs | |
Publication status | Published - 2007 May 28 |
Keywords
- Independence number
- Vertex-disjoint cycles
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics