Results 51 to 60 of about 1,282,765 (250)
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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Planar lattices and planar graphs
Journal of Combinatorial Theory, Series B, 1976 AbstractIt is shown that a finite lattice is planar if and only if the (undirected) graph obtained from its (Hasse) diagram by adding an edge between its least and greatest elements is a planar graph.
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On the planarity of Hanoi graphs
Expositiones Mathematicae, 2002 This note investigates Hanoi graphs \(H^n_m\) which are defined as the state graphs of the well-known game of Hanoi with \(n\) disks and \(m+3\) pegs. It is shown that all those graphs are Hamiltonian and precisely \(H^0_m\), \(H^n_0\), \(H^1_1\) and \(H^2_1\) are planar.
Daniele Parisse, Andreas M. Hinz
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Inapproximability of the Tutte polynomial of a planar graph [PDF]
Computational Complexity, 2009 The Tutte polynomial of a graph G is a two-variable polynomial T(G; x, y) that encodes many interesting properties of the graph. We study the complexity of the following problem, for rationals x and y: given as input a planar graph G, determine T(G; x, y)
L. A. Goldberg, M. Jerrum
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On the planarity of jump graphs
Discrete Mathematics, 2000 Let \(G\) be a graph of size \(m\geq 1\) and let \(F\) and \(H\) be edge-induced subgraphs of \(G\) of size \(k\) with \(1\leq k\leq m\). In the literature is then defined the \(k\)-jump distance from \(F\) to \(H\). For a graph \(G\) of size \(m\geq 1\) and an integer \(k\) with \(1\leq k\leq m\), the \(k\)-jump graph \(J_k(G)\) is defined as a graph ...
Donald W. VanderJagt +2 more
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On the minimum size of maximal IC-plane graphs
AIMS MathematicsA graph is IC-planar if it admits a drawing with at most one crossing per edge so that each vertex is incident to at most one crossing edge, and an IC-plane graph means such a drawing of an IC-planar graph.
Rui Xu
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Every Planar Map Is Four Colorable
Mathematical Solitaires & Games, 2019 As has become standard, the four color map problem will be considered in the dual sense as the problem of whether the vertices of every planar graph (without loops) can be colored with at most four colors in such a way that no pair of vertices which lie ...
K. Appel, W. Haken
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Discrete Applied Mathematics, 1998 The 1-skeleton of a spherical polyhedron might also be viewed as the 1-skeleton of other panelled structures (perhaps having holes, for example). The authors characterize those collections of cycles of a planar graph that bound the panels of hinged-panel structures, and distinguish those arising from spherical polyhedra.
Don Row, James Oxley
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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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Journal of Combinatorial Theory, 1968 AbstractA characterization of the class of planar geodetic graphs is ...
Joel G. Stemple +3 more
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