Results 11 to 20 of about 1,442,532 (348)
Shallow Minors, Graph Products, and Beyond-Planar Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2021 The planar graph product structure theorem of Dujmovi\'{c}, Joret, Micek, Morin, Ueckerdt, and Wood [J. ACM 2020] states that every planar graph is a subgraph of the strong product of a graph with bounded treewidth and a path.
Robert Hickingbotham, D. Wood
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Quantum approximate optimization of non-planar graph problems on a planar superconducting processor [PDF]
Nature Physics, 2020 Faster algorithms for combinatorial optimization could prove transformative for diverse areas such as logistics, finance and machine learning. Accordingly, the possibility of quantum enhanced optimization has driven much interest in quantum technologies.
F. Arute +83 more
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Untangling a Planar Graph [PDF]
Discrete & Computational Geometry, 2009 A straight-line drawing $ $ of a planar graph $G$ need not be plane, but can be made so by \emph{untangling} it, that is, by moving some of the vertices of $G$. Let shift$(G, )$ denote the minimum number of vertices that need to be moved to untangle $ $. We show that shift$(G, )$ is NP-hard to compute and to approximate. Our hardness results extend
Xavier Goaoc +5 more
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CPL-SLAM: Efficient and Certifiably Correct Planar Graph-Based SLAM Using the Complex Number Representation [PDF]
IEEE Transactions on robotics, 2020 In this article, we consider the problem of planar graph-based simultaneous localization and mapping (SLAM) that involves both poses of the autonomous agent and positions of observed landmarks.
Taosha Fan +3 more
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DiGress: Discrete Denoising diffusion for graph generation [PDF]
International Conference on Learning Representations, 2022 This work introduces DiGress, a discrete denoising diffusion model for generating graphs with categorical node and edge attributes. Our model utilizes a discrete diffusion process that progressively edits graphs with noise, through the process of adding ...
Clément Vignac +5 more
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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 +10 more
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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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Mathematical Modelling and Control, 2021 In this paper, we study the problem of partitioning the vertex set of a planar graph with girth restriction into parts, also referred to as color classes, such that each part induces a graph with components of bounded order.
Chunyu Tian, Lei Sun
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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 $Γ_i$
Da Lozzo G., Rutter I.
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The k-subconnectedness of planar graphs
AIMS Mathematics, 2021 A graph G with at least 2k vertices is called k-subconnected if, for any 2k vertices x1,x2,⋯,x2k in G, there are k independent paths joining the 2k vertices in pairs in G.
Zongrong Qin, Dingjun Lou
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