Removable ears of 1-extendable graphs |
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| Authors: | Shaohui Zhai Xiaofeng Guo |
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| Affiliation: | 1.Department of Mathematics and Physics,Xiamen University of Technology,Xiamen,China;2.School of Mathematical Sciences,Xiamen University,Xiamen,China |
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| 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 }
$
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 }
$
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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