TY - JOUR
T1 - Independence number and vertex-disjoint cycles
AU - Egawa, Yoshimi
AU - Enomoto, Hikoe
AU - Jendrol, Stanislav
AU - Ota, Katsuhiro
AU - Schiermeyer, Ingo
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
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
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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 -