Edge covering pseudo-outerplanar graphs with forests

A graph is pseudo-outerplanar if each block has an embedding on the plane in such a way that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. In this paper, we prove that each pseudo-outerplanar graph admits edge decompositions into a linear forest and an outerplanar graph, or a star forest and an outerplanar graph, or two forests and a matching, or max { Δ ( G ) , 4 } matchings, or max { ⌈ Δ ( G ) / 2 ⌉ , 3 } linear forests. These results generalize known results on outerplanar graphs and K 2 , 3 -minor-free graphs, since the class of pseudo-outerplanar graphs is larger than the class of K 2 , 3 -minor-free graphs.