Results 1 to 10 of about 17,845 (164)
Theoretical Computer Science, 2018 We introduce the family of $k$-gap-planar graphs for $k \geq 0$, i.e., graphs that have a drawing in which each crossing is assigned to one of the two involved edges and each edge is assigned at most $k$ of its crossings. This definition is motivated by applications in edge casing, as a $k$-gap-planar graph can be drawn crossing-free after introducing ...
Sang Won Bae, Jinhee Chun, Peter Eades
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A fuzzy soft planar graph with application in image segmentation [PDF]
Scientific ReportsFuzzy sets and soft sets are two distinct mathematical tools used for modeling real-world problems involving uncertainty. In this study, we combine these models to address vagueness and uncertainty within the framework of planar graphs.
Waheed Ahmad Khan +5 more
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Computational Geometry: Theory and Applications, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Prosenjit Bose, FERRÁN Hurtado
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Planar Projections of Graphs [PDF]
Discrete Applied Mathematics, 2020 We introduce and study a new graph representation where vertices are embedded in three or more dimensions, and in which the edges are drawn on the projections onto the axis-parallel planes. We show that the complete graph on $n$ vertices has a representation in $\lceil \sqrt{n/2}+1 \rceil$ planes.
N. R. Aravind, Udit Maniyar
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On families of 2-nearly Platonic graphs
Electronic Journal of Graph Theory and Applications, 2022 A 2-nearly Platonic graph of type (k|d) is a k-regular planar graph with f faces, f − 2 of which are of size d and the remaining two are of sizes d1, d2, both different from d. Such a graph is called balanced if d1 = d2.
Dalibor Froncek +3 more
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Untangling a Planar Graph [PDF]
Discrete & Computational Geometry, 2008 In John Tantalo’s on-line game Planarity the player is given a non-plane straight-line drawing of a planar graph. The aim is to make the drawing plane as quickly as possible by moving vertices. Pach and Tardos have posed a related problem: can any straight-line drawing of any planar graph with n vertices be made plane by vertex moves while keeping ...
Spillner, A., Wolff, A.
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Planar Graphs as VPG-Graphs [PDF]
Journal of Graph Algorithms and Applications, 2013 Summary: A graph is \(B_k\)-VPG when it has an intersection representation by paths in a rectangular grid with at most \(k\) bends (turns). It is known that all planar graphs are \(B_3\)-VPG and this was conjectured to be tight. We disprove this conjecture by showing that all planar graphs are \(B_2\)-VPG.
Steven Chaplick, Torsten Ueckerdt
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Weak Degeneracy of Planar Graphs and Locally Planar Graphs
The Electronic Journal of Combinatorics, 2023 Weak degeneracy is a variation of degeneracy which shares many nice properties of degeneracy. In particular, if a graph $G$ is weakly $d$-degenerate, then for any $(d+1)$-list assignment $L$ of $G$, one can construct an $L$ coloring of $G$ by a modified greedy coloring algorithm.
Ming Han +4 more
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Planarity of Streamed Graphs [PDF]
Theoretical Computer Science, 2015 In this paper we introduce a notion of planarity for graphs that are presented in a streaming fashion. A $\textit{streamed graph}$ is a stream of edges $e_1,e_2,...,e_m$ on a vertex set $V$. A streamed graph is $ω$-$\textit{stream planar}$ with respect to a positive integer window size $ω$ if there exists a sequence of planar topological drawings $Γ_i$
Giordano Da Lozzo, Ignaz Rutter
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On the planar edge-length ratio of planar graphs
Journal of Computational Geometry, 2020 The edge-length ratio of a straight-line drawing of a graph is the ratio between the lengths of the longest and of the shortest edge in the drawing. The planar edge-length ratio of a planar graph is the minimum edge-length ratio of any planar straight ...
Manuel Borrazzo, Fabrizio Frati
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