# Independence number and vertex-disjoint cycles

Yoshimi Egawa, Hikoe Enomoto, Stanislav Jendrol, Katsuhiro Ota, Ingo Schiermeyer

8 被引用数 (Scopus)

## 抄録

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).

本文言語 English 1493-1498 6 Discrete Mathematics 307 11-12 https://doi.org/10.1016/j.disc.2005.11.086 Published - 2007 5 28

## ASJC Scopus subject areas

• 理論的コンピュータサイエンス
• 離散数学と組合せ数学

## フィンガープリント

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