Interval graphs are intersection graphs of closed intervals of the real-line. The well-known
computational problem, called recognition, asks whether an input graph G can be …

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 …

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 …

The partial representation extension problem is a recently introduced generalization of the
recognition problem. A circle graph is an intersection graph of chords of a circle. We study …

In 1969, Roberts introduced proper and unit interval graphs and proved that these classes
are equal. Natural generalizations of unit interval graphs called k-length interval graphs …

The problem of extending partial geometric graph representations such as plane graphs has
received considerable attention in recent years. In particular, given a graph $ G $, a …

For a graph G, a function ψ ψ is called a bar visibility representation of G when for each
vertex v ∈ V (G) v∈ V (G), ψ (v) ψ (v) is a horizontal line segment (bar) and uv ∈ E (G) uv∈ …

Extension Properties of Graphs and Structures Pavel Klavík The main motivation for graph
drawing and geometric representations is finding ways to visualize graphs efficiently to …