Beyond Planar Graphs: Introduction

Hong, Seok‐Hee

doi:10.1007/978-981-15-6533-5_1

Cited by 8 publications

(2 citation statements)

References 37 publications

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“…For further results, consider the surveys and book on beyond planar graph classes [14,23,27], the report on sparsest saturation [24, section 3.2].…”

Section: Related Workmentioning

confidence: 99%

Edge‐minimum saturated k‐planar drawings

Chaplick,

Klute,

Parada

et al. 2024

Journal of Graph Theory

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For a class of drawings of loopless (multi‐)graphs in the plane, a drawing is saturated when the addition of any edge to results in —this is analogous to saturated graphs in a graph class as introduced by Turán and Erdős, Hajnal, and Moon. We focus on ‐planar drawings, that is, graphs drawn in the plane where each edge is crossed at most times, and the classes of all ‐planar drawings obeying a number of restrictions, such as having no crossing incident edges, no pair of edges crossing more than once, or no edge crossing itself. While saturated ‐planar drawings are the focus of several prior works, tight bounds on how sparse these can be are not well understood. We establish a generic framework to determine the minimum number of edges among all ‐vertex saturated ‐planar drawings in many natural classes. For example, when incident crossings, multicrossings and selfcrossings are all allowed, the sparsest ‐vertex saturated ‐planar drawings have edges for any , while if all that is forbidden, the sparsest such drawings have edges for any .

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“…For further results, consider the surveys and book on beyond planar graph classes [14,23,27], the report on sparsest saturation [24, section 3.2].…”

Section: Related Workmentioning

confidence: 99%

Edge‐minimum saturated k‐planar drawings

Chaplick,

Klute,

Parada

et al. 2024

Journal of Graph Theory

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show abstract

“…This motivation is further reinforced by some human cognitive experiments designed to assess users' analytical capabilities when specific types of edge crossings are avoided in graph visualizations. See [15], [16], [17], [18] for surveys or books on the subject.…”

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confidence: 99%

Graphs Drawn With Some Vertices per Face: Density and Relationships

Binucci,

Di Battista,

Didimo

et al. 2024

IEEE Access

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In addition to the content of [1], the present article: (i) contains full proofs and technical details that were omitted or only sketched in [1]; (ii) it contains a related work section; (iii) it contains a new section with results on complete graphs and complete bipartite graphs; (iv) it improves and extends the introduction and the conclusions to better motivate the subject of the paper and to highlight future research directions that can be of interest for the scientific community; (v) it extends the presentation of the results about inclusion relationships; (vi) it contains additional and revised figures, and more than 30 references in the bibliography.

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A Heuristic Approach Towards Drawings of Graphs with High Crossing Resolution

Bekos

Förster

Geckeler

et al. 2018

Lecture Notes in Computer Science

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The crossing resolution of a non-planar drawing of a graph is the value of the minimum angle formed by any pair of crossing edges. Recent experiments have shown that the larger the crossing resolution is, the easier it is to read and interpret a drawing of a graph. However, maximizing the crossing resolution turns out to be an NP-hard problem in general and only heuristic algorithms are known that are mainly based on appropriately adjusting force-directed algorithms. In this paper, we propose a new heuristic algorithm for the crossing resolution maximization problem and we experimentally compare it against the known approaches from the literature. Our experimental evaluation indicates that the new heuristic produces drawings with better crossing resolution, but this comes at the cost of slightly higher aspect ratio, especially when the input graph is large.

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Beyond Planar Graphs: Introduction

Cited by 8 publications

References 37 publications

Edge‐minimum saturated k‐planar drawings

Edge‐minimum saturated k‐planar drawings

Graphs Drawn With Some Vertices per Face: Density and Relationships

A Heuristic Approach Towards Drawings of Graphs with High Crossing Resolution

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