On minimum balanced bipartitions of triangle-free graphs

  • Authors:

  • Haiyan Li;Yanting Liang;Muhuo Liu;Baogang Xu

  • Affiliations:

  • Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China 210046;University of Wisconsin---Fond du Lac, Fond du Lac, USA 54935;Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China 210046 and Department of Applied Mathematics, South China Agricultural University, Guangzhou, C ...;Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, China 210046

  • Venue:
  • Journal of Combinatorial Optimization
  • Year:
  • 2014

Quantified Score

Hi-index 0.00

Visualization

Abstract

A balanced bipartition of a graph G is a partition of V(G) into two subsets V1 and V2 that differ in cardinality by at most 1. A minimum balanced bipartition of G is a balanced bipartition V1, V2 of G minimizing e(V1,V2), where e(V1,V2) is the number of edges joining V1 and V2 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 V1,V2 such that the subgraphs of G induced by V1 and by V2 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).