The even adjacency split problem for graphs Original Research Article

The even adjacency split problem is defined as follows: given an undirected graph, determine whether its vertex set can be partitioned into two dominating sets whose sizes differ by at most one. We show that the problem is NP-complete for general graphs. We also present two algorithms for restricted classes of graphs: first, an algorithm with time complexity linear in the number of edges that finds such a partition for all graphs which contain no isolated vertices and no vertex adjacent to more than two vertices of degree one; and second, an algorithm which determines if such a partition exists for a tree with n vertices in time O(n2).