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

VL - 222

SP - 285

EP - 290

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -