Algorithms and outerplanar conditions for A-trails in plane Eulerian graphs Original Research Article

The problem of finding A-trails in plane Eulerian graphs is NP-complete even for 3-connected graphs, as shown by the first two authors in an earlier paper. In the present paper, we discuss sufficient conditions for the existence of an A-trail in a 2-connected plane Eulerian graph. They generalize the result that simple 2-connected outerplane Eulerian graphs always have A-trails; we give a polynomial algorithm for finding A-trails in such graphs and show that this algorithm also works for certain multigraphs.