Results 21 to 30 of about 1,282,765 (250)
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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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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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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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
doaj +1 more source
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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On the planarity of line Mycielskian graph of a graph
Ratio Mathematica, 2020 The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤ i ≤ q and e, then for 1 ≤ i ≤ q , joining ei' to the neighbours of ei and to e.
Keerthi G. Mirajkar +1 more
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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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The maximum number of pentagons in a planar graph [PDF]
Journal of Graph Theory, 2019 In 1979, Hakimi and Schmeichel considered the problem of maximizing the number of cycles of a given length in an n $n$ ‐vertex planar graph. They precisely determined the maximum number of triangles and four‐cycles and presented a conjecture for the ...
E. Györi +4 more
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Tropically planar graphs [PDF]
Collectanea Mathematica, 2021 28 pages, 29 figures; updated to correct erroneous counts at the end of Section ...
Desmond Coles +4 more
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