REMOVABLE EARS OF 1-EXTENDABLE GRAPHS

Carvalho, Lucchesi and Murty proved that any 1-extendable graph G different from K(2) and C(2n) has at least Delta(G) edge-disjoint removable ears, and any brick G distinct from K(4) and (C(6)) over bar has at least Delta(G) - 2 removable edges, where Delta(G) denotes the maximum degree of G. In this paper, we improve 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 K(2) and C(2n) has at least chi'(G) edge-disjoint removable ears, and any brick G distinct from K(4) and (C(6)) over bar has at least chi'(G)-2 removable edges, where chi'(G) denotes the edge-chromatic number of G.