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Neighborhood Unions for the Existence of Disjoint Chorded Cycles in Graphs

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Abstract

A chorded cycle is a cycle with at least one chord. We prove that if G is a simple graph with order n ≥ 4k and \({|N_G(x)\cup N_G(y)|\geq 4k+1}\) for each nonadjacent pair of vertices x and y, then G contains k vertex-disjoint chorded cycles. The degree condition is sharp in general.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Ningxia University, Ningxia, 750021, People’s Republic of China

    Yunshu Gao

  2. School of Mathematics, Shandong University, Jinan, 250100, People’s Republic of China

    Guojun Li & Jin Yan

Authors
  1. Yunshu Gao
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  2. Guojun Li
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  3. Jin Yan
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Corresponding author

Correspondence to Yunshu Gao.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 11161035), Ningxia Ziran (Grant No. NZ1153) and research grant from Ningxia University (Grant No. ndzr10-19).

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Gao, Y., Li, G. & Yan, J. Neighborhood Unions for the Existence of Disjoint Chorded Cycles in Graphs. Graphs and Combinatorics 29, 1337–1345 (2013). https://doi.org/10.1007/s00373-012-1200-0

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  • DOI: https://doi.org/10.1007/s00373-012-1200-0

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