### Abstract

We give two recursive theorems on n-extendible graphs. A graph G is said to be (k,n)-extendible if every connected induced subgraph of G of order 2k is n-extendible. It is said to be [k,n]-extendible if G -V (H) is n-extendible for every connected induced subgraph H of G of order 2k. In this note we prove that every (k,n)-extendible graph is (k + 1, n + 1)-extendible and that every [k,n]-extendible graph is [k -1,n]-extendible. Both are natural generalizations of recent results by Nishimura ([1, 2]).

Original language | English |
---|---|

Pages (from-to) | 319-323 |

Number of pages | 5 |

Journal | Discrete Mathematics |

Volume | 162 |

Issue number | 1-3 |

Publication status | Published - 1996 Dec 25 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*162*(1-3), 319-323.

**Two recursive theorems on n-extendibility.** / Nishimura, Tsuyoshi; Saito, Akira.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 162, no. 1-3, pp. 319-323.

}

TY - JOUR

T1 - Two recursive theorems on n-extendibility

AU - Nishimura, Tsuyoshi

AU - Saito, Akira

PY - 1996/12/25

Y1 - 1996/12/25

N2 - We give two recursive theorems on n-extendible graphs. A graph G is said to be (k,n)-extendible if every connected induced subgraph of G of order 2k is n-extendible. It is said to be [k,n]-extendible if G -V (H) is n-extendible for every connected induced subgraph H of G of order 2k. In this note we prove that every (k,n)-extendible graph is (k + 1, n + 1)-extendible and that every [k,n]-extendible graph is [k -1,n]-extendible. Both are natural generalizations of recent results by Nishimura ([1, 2]).

AB - We give two recursive theorems on n-extendible graphs. A graph G is said to be (k,n)-extendible if every connected induced subgraph of G of order 2k is n-extendible. It is said to be [k,n]-extendible if G -V (H) is n-extendible for every connected induced subgraph H of G of order 2k. In this note we prove that every (k,n)-extendible graph is (k + 1, n + 1)-extendible and that every [k,n]-extendible graph is [k -1,n]-extendible. Both are natural generalizations of recent results by Nishimura ([1, 2]).

UR - http://www.scopus.com/inward/record.url?scp=0042542467&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042542467&partnerID=8YFLogxK

M3 - Article

VL - 162

SP - 319

EP - 323

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 1-3

ER -