Results 21 to 30 of about 28,365 (265)
Total Coloring of Dumbbell Maximal Planar Graphs
Mathematics, 2022 The Total Coloring Conjecture (TCC) states that every simple graph G is totally (Δ+2)-colorable, where Δ denotes the maximum degree of G. In this paper, we prove that TCC holds for dumbbell maximal planar graphs.
Yangyang Zhou +3 more
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Planar Transitive Graphs [PDF]
The Electronic Journal of Combinatorics, 2018 We prove that the first homology group of every planar locally finite transitive graph $G$ is finitely generated as an $\Aut(G)$-module and we prove a similar result for the fundamental group of locally finite planar Cayley graphs. Corollaries of these results include Droms's theorem that planar groups are finitely presented and Dunwoody's theorem that
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Multiscale planar graph generation
Applied Network Science, 2019 The study of network representations of physical, biological, and social phenomena can help us better understand their structure and functional dynamics as well as formulate predictive models of these phenomena. However, due to the scarcity of real-world
Varsha Chauhan +2 more
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Comparative Study of Planar Octahedron Molecular Structure via Eccentric Invariants
Molecules, 2023 A branch of graph theory that makes use of a molecular graph is called chemical graph theory. Chemical graph theory is used to depict a chemical molecule. A graph is connected if there is an edge between every pair of vertices.
Zheng-Qing Chu +5 more
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A Sufficient Condition for Planar Graphs of Maximum Degree 6 to be Totally 7-Colorable
Discrete Dynamics in Nature and Society, 2020 A total k-coloring of a graph is an assignment of k colors to its vertices and edges such that no two adjacent or incident elements receive the same color.
Enqiang Zhu, Yongsheng Rao
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Total Coloring of Claw-Free Planar Graphs
Discussiones Mathematicae Graph Theory, 2022 A total coloring of a graph is an assignment of colors to both its vertices and edges so that adjacent or incident elements acquire distinct colors. Let Δ(G) be the maximum degree of G.
Liang Zuosong
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From light edges to strong edge-colouring of 1-planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A strong edge-colouring of an undirected graph $G$ is an edge-colouring where every two edges at distance at most~$2$ receive distinct colours. The strong chromatic index of $G$ is the least number of colours in a strong edge-colouring of $G$.
Julien Bensmail +3 more
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An algorithm of graph planarity testing and cross minimization [PDF]
Computer Science Journal of Moldova, 2007 This paper presents an overview on one compartment from the graph theory, called graph planarity testing. It covers the fundamental concepts and important work in this area.
Vitalie Cotelea, Stela Pripa
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Computing Planarity in Computable Planar Graphs
Graphs and Combinatorics, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Oscar Levin, Taylor McMillan
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Treewidth 2 in the Planar Graph Product Structure Theorem [PDF]
Discrete Mathematics & Theoretical Computer ScienceWe prove that every planar graph is contained in $H_1\boxtimes H_2\boxtimes K_2$ for some graphs $H_1$ and $H_2$ both with treewidth 2. This resolves a question of Liu, Norin and Wood [arXiv:2410.20333]. We also show this result is best possible: for any
Marc Distel +4 more
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