A Linear Time Algorithm for Graph Partition Problems

In this paper we present an O( I V I + I E I) time algorithm which partitions the set of vertices of an undirected graph G = (I’, E) with maximum degree A and minimum degree 6 to {A, x} such that the following hold. (8 The number of edges with one end point in A and the other end point in x is at least IEl/2. (ii> The difference between the number of vertices in A and the number of vertices in Ais 0 if I V I is even, and is 1 if I V I is odd. (iii) The absolute value of the difference between the number of edges with both end points in A and the number of edges with both end points in x is at most (A 6)/2 if I V I is even, and is at most (A + 1)/2 if I V I is odd.