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 |
Fingerprint
Keywords
- Independence number
- Vertex-disjoint cycles
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science
Cite this
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 journal › Article
}
TY - JOUR
T1 - Independence number and vertex-disjoint cycles
AU - Egawa, Yoshimi
AU - Enomoto, Hikoe
AU - Jendrol, Stanislav
AU - Ota, Katsuhiro
AU - Schiermeyer, Ingo
PY - 2007/5/28
Y1 - 2007/5/28
N2 - 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).
AB - 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).
KW - Independence number
KW - Vertex-disjoint cycles
UR - http://www.scopus.com/inward/record.url?scp=33947243416&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33947243416&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2005.11.086
DO - 10.1016/j.disc.2005.11.086
M3 - Article
AN - SCOPUS:33947243416
VL - 307
SP - 1493
EP - 1498
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
IS - 11-12
ER -