REMOVABLE EARS OF 1-EXTENDABLE GRAPHS

Carvalho,Lucchesi and Murty proved that any 1-extendable graph G different from Kand Chas at least Δ(G)edge-disjoint removable ears,and any brick G distinct from Kand■hasat least Δ(G)-2 removable edges,where Δ(G)denotes the maximum degree of G.In this paper,weimprove the lower bounds for numbers of removable ears and removable edges of 1-extendable graphs.It is proved that any 1-extendable graph G different from Kand Chas at least χ′(G)edge-disjointremovable ears,and any brick G distinct from Kand■has at least χ′(G)-2 removable edges,whereχ′(G)denotes the edge-chromatic number of G.