Approximation Algorithms for Maximally Balanced Connected Graph Partition

Given a connected graph $$G = (V, E)$$ , we seek to partition the vertex set V into k non-empty parts such that subgraph induced by each part is connected, and maximally balanced in way maximum cardinality of these minimized. We refer this problem as min-max denote it -BGP. The vertex-weighted version on trees has been studied since about four decades ago, which admits linear time exact algorithm. 2-BGP 3-BGP admit 5/4-approximation 3/2-approximation, respectively. When $$k \ge 4$$ no approximability result exists for -BGP, i.e., unweighted variant, except trivial k-approximation. In paper, present another 3/2-approximation then extend become k/2-approximation any fixed 3$$ . Furthermore, 4-BGP, propose an improved 24/13-approximation. To purposes, have designed several local improvement operations, could find more applications related problems.