Independence number and vertex-disjoint cycles

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

Research output: Contribution to journalArticle

7 Citations (Scopus)

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 languageEnglish
Pages (from-to)1493-1498
Number of pages6
JournalDiscrete Mathematics
Volume307
Issue number11-12
DOIs
Publication statusPublished - 2007 May 28

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Independence number
Disjoint
Cycle
Vertex of a graph
Graph in graph theory
Integer

Keywords

  • Independence number
  • Vertex-disjoint cycles

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Egawa, Y., Enomoto, H., Jendrol, S., Ota, K., & Schiermeyer, I. (2007). Independence number and vertex-disjoint cycles. Discrete Mathematics, 307(11-12), 1493-1498. https://doi.org/10.1016/j.disc.2005.11.086

Independence number and vertex-disjoint cycles. / Egawa, Yoshimi; Enomoto, Hikoe; Jendrol, Stanislav; Ota, Katsuhiro; Schiermeyer, Ingo.

In: Discrete Mathematics, Vol. 307, No. 11-12, 28.05.2007, p. 1493-1498.

Research output: Contribution to journalArticle

Egawa, Y, Enomoto, H, Jendrol, S, Ota, K & Schiermeyer, I 2007, 'Independence number and vertex-disjoint cycles', Discrete Mathematics, vol. 307, no. 11-12, pp. 1493-1498. https://doi.org/10.1016/j.disc.2005.11.086
Egawa Y, Enomoto H, Jendrol S, Ota K, Schiermeyer I. Independence number and vertex-disjoint cycles. Discrete Mathematics. 2007 May 28;307(11-12):1493-1498. https://doi.org/10.1016/j.disc.2005.11.086
Egawa, Yoshimi ; Enomoto, Hikoe ; Jendrol, Stanislav ; Ota, Katsuhiro ; Schiermeyer, Ingo. / Independence number and vertex-disjoint cycles. In: Discrete Mathematics. 2007 ; Vol. 307, No. 11-12. pp. 1493-1498.
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