Several problems, including the maximum integral two-flow problem, are
known to be NP-complete, but efficiently solvable for planar graphs.
In this paper, we extend the algorithm for maximum integral two-flow i
n planar graphs to certain undirected K-3,K-3-free graphs (graphs not
containing any subgraph homeomorphic to K-3,K-3). For such graphs, we
provide an O(n) algorithm for determining a maximum integral two-flow
of a value not less than the value of a maximum two-flow minus two. (C
) 1998 John Wiley & Sons, Inc. Networks 32: 67-76, 1998.