Independence number and vertex-disjoint cycles

1Citations
Citations of this article
9Readers
Mendeley users who have this article in their library.

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). © 2006.

Cite

CITATION STYLE

APA

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

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free