TY - JOUR

T1 - A recursive theorem on matching extension

AU - Chan, Chi I.

AU - Nishimura, Tsuyoshi

N1 - Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2000

Y1 - 2000

N2 - A graph G having a perfect matching (or I-factor) is called n-fextendable if every matching of size n is extended to a I-factor. Further, G is said to be 〈r: m, n 〉-extendable if, for every connected subgraph S of order 2r for which G \ V(S) is connected, S is m-extendable and G \ V(S) is nextendable. We prove the following: Let p, r, m, and n be positive integers with p - r > nand r > m. Then every 2-connected 〈r: m, n〉-extendable graph of order 2p is 〈r + 1: m + 1, n - 1〉-extendable.

AB - A graph G having a perfect matching (or I-factor) is called n-fextendable if every matching of size n is extended to a I-factor. Further, G is said to be 〈r: m, n 〉-extendable if, for every connected subgraph S of order 2r for which G \ V(S) is connected, S is m-extendable and G \ V(S) is nextendable. We prove the following: Let p, r, m, and n be positive integers with p - r > nand r > m. Then every 2-connected 〈r: m, n〉-extendable graph of order 2p is 〈r + 1: m + 1, n - 1〉-extendable.

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M3 - Article

AN - SCOPUS:84885905951

SN - 1034-4942

VL - 21

SP - 49

EP - 55

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

ER -