Algorithms for 2-balanced connected k-partition problem in graphs - Yu, Junran; Hu, Jing; Gao, Jiaquan; Du, Donglei; Zhang, Xiaoyan (Journal of combinatorial optimization, 2025)
Motivated by the result of balanced connected graph edge partition problem for trees, we investigate the 2-balanced connected graph vertex k -partition problem. This paper leverages the charity vertex method and proposes several algorithms for 2-balanced vertex-connected partitioning. Furthermore, we prove that these algorithms are polynomial-time solvable on degree-bounded graphs, thereby refining and extending the results of Caragiannis et al.