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]).
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics