TY - JOUR
T1 - On 1-factors and matching extension
AU - Nishimura, Tsuyoshi
N1 - Funding Information:
I would like to acknowledge to the referees for their comments. This work was supported by the Grant in Aid for Scienti c Research of the Ministry of Education, Science and Culture of Japan under the grant number: YSE(A)10740059 (1998).
PY - 2000/7/28
Y1 - 2000/7/28
N2 - We prove the following: (1) Let G be a graph with a 1-factor and let F be an arbitrary 1-factor of G. If G \ {a,b} is k-extendable for each ab ∈ F, then G is k-extendable. (2) Let G be a graph and let M be an arbitrary maximal matching of G. If G \ {a, b} is k-factor-critical for each ab ∈ M, then G is k-factor-critical.
AB - We prove the following: (1) Let G be a graph with a 1-factor and let F be an arbitrary 1-factor of G. If G \ {a,b} is k-extendable for each ab ∈ F, then G is k-extendable. (2) Let G be a graph and let M be an arbitrary maximal matching of G. If G \ {a, b} is k-factor-critical for each ab ∈ M, then G is k-factor-critical.
KW - 1-factor
KW - Matching
KW - k-extendable
KW - k-factor-critical
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U2 - 10.1016/S0012-365X(00)00057-1
DO - 10.1016/S0012-365X(00)00057-1
M3 - Article
AN - SCOPUS:0347646890
SN - 0012-365X
VL - 222
SP - 285
EP - 290
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 1-3
ER -