Statuses and double branch weights of quadrangular outerplanar graphs

Quadrangular embeddings of complete graphs∗

Hartsfield and Ringel proved that a complete graph Kn has an orientable quadrangular embedding if n ≡ 5 (mod 8), and has a nonorientable quadrangular embedding if n ≥ 9 and n ≡ 1 (mod 4). We complete the characterization of complete graphs admitting quadrangular embeddings by showing that Kn has an orientable quadrilateral embedding if n ≡ 0 (mod 8), and has a nonorientable quadrilateral embedd...

Pathwidth of outerplanar graphs

We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [2], after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual plus two, conjectured that there exists a constant c such that the pathwidth of every biconnected...

Drawing outerplanar graphs

It is shown that for any outerplanar graph G there is a one to one mapping of the vertices of G to the plane, so that the number of distinct distances between pairs of connected vertices is at most three. This settles a problem of Carmi, Dujmovic, Morin and Wood. The proof combines (elementary) geometric, combinatorial, algebraic and probabilistic arguments.

Generating Random Outerplanar Graphs

Monitoring maximal outerplanar graphs

In this paper we define a new concept of monitoring the elements of triangulation graphs by faces. Furthermore, we analyze this, and other monitoring concepts (by vertices and by edges), from a combinatorial point of view, on maximal outerplanar graphs.