Edge covering pseudo-outerplanar graphs with forests

A graph is called 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{∆(G), 4} matchings, or max{⌈∆(G)/2⌉, 3} linear forests. These results generalize some ones on outerplanar graphs and K2,3-minor-free graphs, since the class of pseudo-outerplanar graphs is a larger class than the one of K2,3-minor-free graphs.