On the edge-length ratio of outerplanar graphs

On the Edge-Length Ratio of Outerplanar Graphs

We show that any outerplanar graph admits a planar straightline drawing such that the length ratio of the longest to the shortest edges is strictly less than 2. This result is tight in the sense that for any > 0 there are outerplanar graphs that cannot be drawn with an edge-length ratio smaller than 2 − . We also show that every bipartite outerplanar graph has a planar straight-line drawing wit...

On interval edge-colorings of outerplanar graphs

A proper edge-coloring of a graph G with colors 1, . . . , t is called an interval t-coloring if the colors of edges incident to any vertex of G form an interval of integers. A graph G is interval colorable if it has an interval t-coloring for some positive integer t. For an interval colorable graph G, the least value of t for which G has an interval t-coloring is denoted by w(G). A graph G is ...

On Edge-Graceful and Edge-Magic Maximal Outerplanar Graphs

Let G be a (p,q)-graph in which the edges are labeled 1,2,3,...q. The vertex sum for a vertex v is the sum of the labels of the incident edges at v. If G can be labeled so that the vertex sums are distinct, mod p, then G is said to be edgegraceful. If the edges of G can be labeled 1,2,3,...q so that the vertex sums are constant, mod p, then G is said to be edgemagic. It is conjectured by Lee [9...

List Edge Colorings of Outerplanar Graphs

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 outerpla...