Abstract
Carvalho, Lucchesi and Murty proved that any 1-extendable graph G different from K 2 and C 2n has at least Δ(G) edge-disjoint removable ears, and any brick G distinct from K 4 and \( \overline {C_6 } \) has at least Δ(G) − 2 removable edges, where Δ(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 χ′(G) edge-disjoint removable ears, and any brick G distinct from K 4 and \( \overline {C_6 } \) has at least χ′(G) − 2 removable edges, where χ′(G) denotes the edge-chromatic number of G.
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