Simultaneous embedding is concerned with simultaneously representing a series of graphs
sharing some or all vertices. This forms the basis for the visualization of dynamic graphs and …

In this article, we define and study the new problem of Simultaneous PQ-Ordering. Its input
consists of a set of PQ-trees, which represent sets of circular orders of their leaves, together …

We study the following problem: given a planar graph G and a planar drawing (embedding)
of a subgraph of G, can such a drawing be extended to a planar drawing of the entire graph …

Chordal graphs are intersection graphs of subtrees of a tree T. We investigate the complexity
of the partial representation extension problem for chordal graphs. A partial representation …

Abstract Let G=(V, E) be a directed graph and ℓ: V→[k]:={1,…, k} a level assignment such
that ℓ (u)< ℓ (v) for all directed edges (u, v)∊ E. A level planar drawing of G is a drawing of G …

The recently introduced problem of extending partial interval representations asks, for an
interval graph with some intervals pre-drawn by the input, whether the partial representation …

Algorithmic extension problems of partial graph representations such as planar graph
drawings or geometric intersection representations are of growing interest in topological …

Function graphs are graphs representable by intersections of continuous real-valued
functions on the interval [0, 1] and are known to be exactly the complements of comparability …

Abstract A simple drawing D (G) of a graph G is one where each pair of edges share at most
one point: either a common endpoint or a proper crossing. An edge e in the complement of …

In this paper we study the computational complexity of the Upward Planarity Extension
problem, which takes as input an upward planar drawing Γ H of a subgraph H of a directed …