Graph Planarity by Replacing Cliques with Paths

Angelini, Patrizio; Eades, Peter; Hong, Seok‐Hee; Klein, Karsten; Kobourov, Stephen G.; Liotta, Giuseppe; Navarra, Alfredo; Tappini, Alessandra

doi:10.3390/a13080194

Cited by 8 publications

(4 citation statements)

References 17 publications

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“…In [1], the authors faced a typical problem concerning the visual analysis of realworld networks. To this end, they introduce and study the following beyond-planarity problem that they call h-CLIQUE2PATH PLANARITY.…”

Section: Special Issuementioning

confidence: 99%

Special Issue on “Graph Algorithms and Applications”

Cicerone

Stefano

2021

Algorithms

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The mixture of data in real life exhibits structure or connection property in nature. Typical data include biological data, communication network data, image data, etc. Graphs provide a natural way to represent and analyze these types of data and their relationships. For instance, more recently, graphs have found new applications in solving problems for emerging research fields such as social network analysis, design of robust computer network topologies, frequency allocation in wireless networks, and bioinformatics. Unfortunately, the related algorithms usually suffer from high computational complexity, since some of these problems are NP-hard. Therefore, in recent years, many graph models and optimization algorithms have been proposed to achieve a better balance between efficacy and efficiency. The aim of this Special Issue is to provide an opportunity for researchers and engineers from both academia and the industry to publish their latest and original results on graph models, algorithms, and applications to problems in the real world, with a focus on optimization and computational complexity.

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Section: Special Issuementioning

confidence: 99%

Special Issue on “Graph Algorithms and Applications”

Cicerone

Stefano

2021

Algorithms

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“…Hybrid visualizations have also been exploited in the context of dynamic network analysis (see, e.g., [15,32,55]). We finally mention several theoretical results on hybrid visualizations that concentrate on the complexity of minimizing the number of intercluster edge crossings (see, e.g., [6,7,8,17,22,23,24,39,41]).…”

Section: Related Workmentioning

confidence: 99%

“…1(c)). After the introduction of NodeTrix, hybrid visualizations have become an emerging topic in graph drawing and network visualization, and inspired an array of both theoretical and application results (see, e.g., [7,8,9,11,14,22,23,24,33,39,41,59]).…”

Section: Introductionmentioning

confidence: 99%

A User Study on Hybrid Graph Visualizations

Giacomo¹,

Didimo²,

Fabrizio³

et al. 2021

Preprint

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Hybrid visualizations mix different metaphors in a single layout of a network. In particular, the popular NodeTrix model, introduced by Henry, Fekete, and McGuffin in 2007, combines node-link diagrams and matrix-based representations to support the analysis of real-world networks that are globally sparse but locally dense. That idea inspired a series of works, proposing variants or alternatives to NodeTrix. We present a user study that compares the classical node-link model and three hybrid visualization models designed to work on the same types of networks. The results of our study provide interesting indications about advantages/drawbacks of the considered models on performing classical tasks of analysis. At the same time, our experiment has some limitations and opens up to further research on the subject.

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“…Graph theory has been developed widely in both theory and application (see [1][2][3][4][5][6][7]). According to [8], regarding the application side, graph theory plays a vital role as it is at the foundations, for instance, of the internet, parallel computing, distributed computing, molecular topology, dynamics, energy, electricity, and electronic circuit design.…”

Section: Introductionmentioning

confidence: 99%

Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths

et al. 2022

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Let Γ=(VΓ,EΓ) be a simple undirected graph with finite vertex set VΓ and edge set EΓ. A total n-labeling α:VΓ∪EΓ→{1,2,…,n} is called a total edge irregular labeling on Γ if for any two different edges xy and x′y′ in EΓ the numbers α(x)+α(xy)+α(y) and α(x′)+α(x′y′)+α(y′) are distinct. The smallest positive integer n such that Γ can be labeled by a total edge irregular labeling is called the total edge irregularity strength of the graph Γ. In this paper, we provide the total edge irregularity strength of some asymmetric graphs and some symmetric graphs, namely generalized arithmetic staircase graphs and generalized double-staircase graphs, as the generalized forms of some existing staircase graphs. Moreover, we give the construction of the corresponding total edge irregular labelings.

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Graph Planarity by Replacing Cliques with Paths

Cited by 8 publications

References 17 publications

Special Issue on “Graph Algorithms and Applications”

Special Issue on “Graph Algorithms and Applications”

A User Study on Hybrid Graph Visualizations

Generalized Arithmetic Staircase Graphs and Their Total Edge Irregularity Strengths

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