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Bipartition of graph under degree constraints

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Abstract

Let G be a graph, let s be a positive integer, and let X be a subset of V (G). Denote δ(X) to be the minimum degree of the subgraph G[X] induced by X. A partition (X, Y) of V (G) is called s-good if min{δ(X), δ(Y)} ⩾ s. In this paper, we strengthen a result of Maurer and a result of Arkin and Hassin, and prove that for any positive integer k with 2 ⩽ k ⩽ |V (G)| − 2, every connected graph G with δ(G) ⩾ 2 admits a 1-good partition (X, Y ) such that |X| = k and |Y | = |V (G)| − k, and δ(X) + δ(Y) ⩾ δ(G) − 1.

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Authors and Affiliations

  1. Department of Applied Mathematics, South China Agricultural University, Guangzhou, 510642, China

    MuHuo Liu

  2. Institute of Mathematics, School of Mathematical Sciences, Nan**g Normal University, Nan**g, 210023, China

    BaoGang Xu

Authors
  1. MuHuo Liu
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  2. BaoGang Xu
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Correspondence to BaoGang Xu.

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Liu, M., Xu, B. Bipartition of graph under degree constraints. Sci. China Math. 58, 869–874 (2015). https://doi.org/10.1007/s11425-014-4915-y

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  • DOI: https://doi.org/10.1007/s11425-014-4915-y

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