Results 1 to 10 of about 1,482,477 (319)
The Odd Chromatic Number of a Planar Graph is at Most 8 [PDF]
Graphs and Combinatorics, 2022 Petruševski and Škrekovski recently introduced the notion of an odd colouring of a graph: a proper vertex colouring of a graph G is said to be odd if for each non-isolated vertex $$x \in V(G)$$ x ∈ V ( G ) there exists a colour c appearing an odd number ...
J. Petr, Julien Portier
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The structure and the list 3-dynamic coloring of outer-1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 An outer-1-planar graph is a graph admitting a drawing in the plane so that all vertices appear in the outer region of the drawing and every edge crosses at most one other edge.
Yan Li, Xin Zhang
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An improved planar graph product structure theorem [PDF]
Electronic Journal of Combinatorics, 2021 Dujmović, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every planar graph $G$ there is a graph $H$ with treewidth at most 8 and a path $P$ such that $G\subseteq H\boxtimes P$. We improve this result by replacing "treewidth at most
T. Ueckerdt, D. Wood, Wendy Yi
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Improved product structure for graphs on surfaces [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 Dujmovi\'c, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved that for every graph $G$ with Euler genus $g$ there is a graph $H$ with treewidth at most 4 and a path $P$ such that $G\subseteq H \boxtimes P \boxtimes K_{\max\{2g,3\}}$. We improve
Marc Distel +3 more
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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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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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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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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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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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