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On the Strong Equitable Vertex 2-Arboricity of Complete Bipartite Graphs

Author

Listed:
  • Fangyun Tao

    (Department of Applied Mathematics, College of Science, Nanjing Forestry University, Nanjing 210037, China)

  • Ting Jin

    (Department of Applied Mathematics, College of Science, Nanjing Forestry University, Nanjing 210037, China)

  • Yiyou Tu

    (School of Materials Science and Engineering, Southeast University, Nanjing 211189, China)

Abstract

An equitable partition of a graph G is a partition of the vertex set of G such that the sizes of any two parts differ by at most one. The strong equitable vertexk - arboricity of G , denoted by v a k ≡ ( G ) , is the smallest integer t such that G can be equitably partitioned into t ′ induced forests for every t ′ ≥ t , where the maximum degree of each induced forest is at most k . In this paper, we provide a general upper bound for v a 2 ≡ ( K n , n ) . Exact values are obtained in some special cases.

Suggested Citation

  • Fangyun Tao & Ting Jin & Yiyou Tu, 2020. "On the Strong Equitable Vertex 2-Arboricity of Complete Bipartite Graphs," Mathematics, MDPI, vol. 8(10), pages 1-6, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1778-:d:427839
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    References listed on IDEAS

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    1. Xin Zhang & Bei Niu, 2020. "Equitable partition of graphs into induced linear forests," Journal of Combinatorial Optimization, Springer, vol. 39(2), pages 581-588, February.
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