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Removable ears of 1-extendable graphs

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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 \( \overline {C_6 } \) 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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Authors and Affiliations

  1. Department of Mathematics and Physics, Xiamen University of Technology, Xiamen, 361024, China

    Shaohui Zhai

  2. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Xiaofeng Guo

Authors
  1. Shaohui Zhai
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  2. Xiaofeng Guo
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Corresponding author

Correspondence to Xiaofeng Guo.

Additional information

This research was supported by the National Science Foundation of China under Grant No. 10831001 and the Fujian Provincial Department of Education under Grant No. JA08223.

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Zhai, S., Guo, X. Removable ears of 1-extendable graphs. J Syst Sci Complex 23, 372–378 (2010). https://doi.org/10.1007/s11424-010-7122-0

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  • DOI: https://doi.org/10.1007/s11424-010-7122-0

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