Removable ears of 1-extendable graphs

Carvalho, Lucchesi and Murty proved that any 1-extendable graph G different from K2 and C2n has at least Δ(G) edge-disjoint removable ears, and any brick G distinct from K4 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline {C_6 } $$\end{document} 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 K2 and C2n has at least χ′(G) edge-disjoint removable ears, and any brick G distinct from K4 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline {C_6 } $$\end{document} has at least χ′(G) − 2 removable edges, where χ′(G) denotes the edge-chromatic number of G.