Light graphs in families of outerplanar graphs Original Research Article

We prove that every 2-connected outerplanar graph of order at least k (image) contains a path on k vertices with all vertices of degree at most image and a path on k vertices with degree sum at most image. Further, every 2-connected outerplanar graph without adjacent vertices with degree sum image contains a triangle image with vertices of degrees 2, 4 and b, image, and a 3-star image with central vertex of degree 4 and remaining vertices of degrees 2, 2 and b, image. Moreover, all bounds are best possible.