The structure and the list 3-dynamic coloring of outer-1-planar graphs

An outer-1-planar graph is a admitting drawing in the plane so that all vertices appear outer region of and every edge crosses at most one other edge. This paper establishes local structure graphs by proving each contains seventeen fixed configurations, list those configurations minimal sense for configuration there exist containing this do not contain any another sixteen configurations. There are two interesting applications structural theorem. First all, we conclude (resp. maximal) minimum degree least 2 has an with sum degrees its end-vertices being 9 7), upper bound sharp. On hand, show 3-dynamic chromatic number 6, best possible.