A local neighbourhood condition for n-extendable graphs

CIHNA Let v E V( G). VI/e define tha.t if for each vertex v E 8)1 ISI+2n. then G JUJIU"-',-"Ln conditions for n-extendable in paper a order v such that n S (II and any n lnCLeu,enaelU and let n be a n-extendable G 01 G are contained in a of vertices of G \Ve define the InCI€'lJ'enaellt set in U k }. of odd components of G. All and notation not defined in this paper are from Since Plummer introduced the of n-extendable much work has been done on this see [5], Lou introduced sufficient condition for n~extendable in terms of the rlnr,p'l'!~p1'H'P and some other sufficient conditions for n-extendable However there are not ma.ny known sufficient conditions for n-extendable Australasian Journal of Combinatorics 14 (1996), pp. 229-233 + A~J + ... + (kmt+ k) So ki + k· J km ; + tk. (2) Claim 2: k, :$ 2.::::1 kmj • We prove kmj ~ k;. (i = 1,2, ... ,t) by induction, and then Claim 2 follows. By the defini tion of km jl we have km 1 2:: k 1. 230