Abstract. Planar drawings of clustered graphs are considered. We introduce the notion of completely connected clustered graphs, i.e. hierarchically clustered graphs that have the p...
In this paper, we show that the dimension of the adjacency poset of a planar graph is at most 8. From below, we show that there is a planar graph whose adjacency poset has dimensio...
The line index of a graph G is the smallest k such that the kth iterated line graph of G is nonplanar. We show that the line index of a graph is either innite or it is at most 4....
Abstract. We present a linear-time algorithm for solving the simultaneous embedding problem with fixed edges (SEFE) for a planar graph and a pseudoforest (a graph with at most one...
J. Joseph Fowler, Carsten Gutwenger, Michael J&uum...