Rectangle-visibility representations of bipartite graphs

Dean, Alice M.; Hutchinson, Joan P.

doi:10.1007/3-540-58950-3_367

Cited by 28 publications

(27 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, graphs with thickness two have drawn some attention in the ®eld of graph-drawing, where they are used in the study of so-called rectangle-visibility graphs [20,27].…”

Section: Ae ç Xmentioning

confidence: 99%

The Thickness of Graphs: A Survey

Mutzel

Odenthal

Scharbrodt³

1998

Graphs Comb

View full text Add to dashboard Cite

We give a state-of-the-art survey of the thickness of a graph from both a theoretical and a practical point of view. After summarizing the relevant results concerning this topological invariant of a graph, we deal with practical computation of the thickness. We present some modi®cations of a basic heuristic and investigate their usefulness for evaluating the thickness and determining a decomposition of a graph in planar subgraphs.

show abstract

“…Moreover, graphs with thickness two have drawn some attention in the ®eld of graph-drawing, where they are used in the study of so-called rectangle-visibility graphs [20,27].…”

Section: Ae ç Xmentioning

confidence: 99%

The Thickness of Graphs: A Survey

Mutzel

Odenthal

Scharbrodt³

1998

Graphs Comb

View full text Add to dashboard Cite

show abstract

“…The 4-cycle (see Figure la) does not have a noncollinear barvisibility layout; Figure 3 shows a (collinear) rectangle-visbility layout of K4,4 minus an edge; by a result in [3] it has no noncollinear layout, but a noncollinear layout of/{4,4 minus two edges is shown in Figure 10. It is easy to see that noncollinear bar-visibility graphs are a subclass of strong bar-visibility graphs, which are in turn a subclass of bar-visibility graphs; analogous inclusions hold in the case of rectangle-visibility graphs.…”

Section: Collinear and Noncollinear Layoutsmentioning

confidence: 99%

“…Tamassia and Tollis [12] show that this subclass ordering for bar-visibility graphs is strict. In [3] Dean and Hutchinson conjecture that the analogous subclass ordering for rectanglevisibility graphs is also strict, and they show that noncollinear rectangle-visibility graphs form a strict subclass of strong rectangle-visibility graphs. Figure 3 shows a strong layout of a graph that has no noncollinear layout.…”

Section: Collinear and Noncollinear Layoutsmentioning

confidence: 99%

On rectangle visibility graphs

Bose

Dean

Hutchinson

et al. 1997

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. We study the problem of drawing a graph in the plane so that the vertices of the graph are rectangles that are aligned with the axes, and the edges of the graph are horizontal or vertical lines-of-sight. Such a drawing is useful, for example, when the vertices of the graph contain information that we wish displayed on the drawing; it is natural to write this information inside the rectangle corresponding to the vertex.We call a graph that can be drawn in this fashion a rectangle-visibility graph, or RVG. Our goal is to find classes of graphs that are RVGs.We obtain several results:1. For 1 < k < 4, k-trees are RVGs. 2. Any graph that can be decomposed into two caterpillar forests is an RVG. 3. Any graph whose vertices of degree four or more form a distance-two independent set is an RVG. 4. Any graph with maximum degree four is an RVG. Our proofs are constructive and yield linear-time layout algorithms.

show abstract

“…The notion of ortho-polygon visibility representation generalizes the classical concept of rectangle visibility representation, that is, in fact, an OPVR with vertex complexity zero (see, e.g., [3,6,14,17,18]). In this context, Biedl et al [3] characterize the 1-plane graphs that admit a rectangle visibility representation in terms of forbidden subgraphs, called B-, T-, and W-configurations (see for examples and Section 2 for definitions).…”

Section: Introductionmentioning

confidence: 99%

Ortho-Polygon Visibility Representations of 3-Connected 1-Plane Graphs

Liotta

Montecchiani

Tappini

2018

Lecture Notes in Computer Science

View full text Add to dashboard Cite

An ortho-polygon visibility representation Γ of a 1-plane graph G (OPVR of G) is an embedding preserving drawing that maps each vertex of G to a distinct orthogonal polygon and each edge of G to a vertical or horizontal visibility between its end-vertices. The representation Γ has vertex complexity k if every polygon of Γ has at most k reflex corners. It is known that 3-connected 1-plane graphs admit an OPVR with vertex complexity at most twelve, while vertex complexity at least two may be required in some cases. In this paper, we reduce this gap by showing that vertex complexity five is always sufficient, while vertex complexity four may be required in some cases. These results are based on the study of the combinatorial properties of the B-, T-, and W-configurations in 3-connected 1-plane graphs. An implication of the upper bound is the existence of aÕ(n 10 7 )-time drawing algorithm that computes an OPVR of an n-vertex 3-connected 1-plane graph on an integer grid of size O(n) × O(n) and with vertex complexity at most five. Research supported in part by: "Algoritmi e sistemi di analisi visuale di reti complesse e di grandi dimensioni" -Ricerca di Base 2018, Dip. Ingegneria -Univ. Perugia. arXiv:1807.01247v2 [cs.DS] 2 Aug 2018Concerning the upper bound stated in Theorem 1, the main difference between our approach and the one in [8] is that we do not aim at removing all crossings so to make G planar. Instead, we define a subset F of the B-, T-, and

show abstract

Rectangle-visibility representations of bipartite graphs

Cited by 28 publications

References 13 publications

The Thickness of Graphs: A Survey

The Thickness of Graphs: A Survey

On rectangle visibility graphs

Ortho-Polygon Visibility Representations of 3-Connected 1-Plane Graphs

Contact Info

Product

Resources

About