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On minimum balanced bipartitions of triangle-free graphs

Author

Listed:
  • Haiyan Li

    (Nanjing Normal University)

  • Yanting Liang

    (University of Wisconsin–Fond du Lac)

  • Muhuo Liu

    (Nanjing Normal University
    South China Agricultural University)

  • Baogang Xu

    (Nanjing Normal University)

Abstract

A balanced bipartition of a graph G is a partition of V(G) into two subsets V 1 and V 2 that differ in cardinality by at most 1. A minimum balanced bipartition of G is a balanced bipartition V 1, V 2 of G minimizing e(V 1,V 2), where e(V 1,V 2) is the number of edges joining V 1 and V 2 and is usually referred to as the size of the bipartition. In this paper, we show that every 2-connected graph G admits a balanced bipartition V 1,V 2 such that the subgraphs of G induced by V 1 and by V 2 are both connected. This yields a good upper bound to the size of minimum balanced bipartition of sparse graphs. We also present two upper bounds to the size of minimum balanced bipartitions of triangle-free graphs which sharpen the corresponding bounds of Fan et al. (Discrete Math. 312:1077–1083, 2012).

Suggested Citation

  • Haiyan Li & Yanting Liang & Muhuo Liu & Baogang Xu, 2014. "On minimum balanced bipartitions of triangle-free graphs," Journal of Combinatorial Optimization, Springer, vol. 27(3), pages 557-566, April.
    • Handle: RePEc:spr:jcomop:v:27:y:2014:i:3:d:10.1007_s10878-012-9539-y
    DOI: 10.1007/s10878-012-9539-y
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    Cited by:

    1. Shufei Wu & Jianfeng Hou, 2018. "Partitioning dense uniform hypergraphs," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 48-63, January.
    2. Muhuo Liu & Baogang Xu, 2016. "On judicious partitions of graphs," Journal of Combinatorial Optimization, Springer, vol. 31(4), pages 1383-1398, May.

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