Results 41 to 50 of about 2,427,282 (299)
Journal of Graph Algorithms and Applications, 2017 We introduce a new type of graph drawing called "rook-drawing". A rook-drawing of a graph $G$ is obtained by placing the $n$ nodes of $G$ on the intersections of a regular grid, such that each row and column of the grid supports exactly one node. This paper focuses on rook-drawings of planar graphs. We first give a linear algorithm to compute a planar
Auber, David +3 more
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Rook-Drawing for Plane Graphs [PDF]
, 2015 Motivated by visualization of large graphs, we introduce a new type of graph drawing called "rook-drawing". A rook-drawing of a graph G is obtained by placing the n nodes of G on the intersections of a regular grid, such that each row and column of the grid supports exactly one node. This paper focuses on rook-drawings of planar graphs. We first give a
Auber, David +3 more
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Flat Foldings of Plane Graphs with Prescribed Angles and Edge Lengths [PDF]
International Symposium Graph Drawing and Network Visualization, 2014 When can a plane graph with prescribed edge lengths and prescribed angles from among {0,180i¾?, 360i¾?} be folded flat to lie in an infinitesimally thick line, without crossings?
Zachary Abel +5 more
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Graph polynomials and paintability of plane graphs
Discrete Applied Mathematics, 2022 There exists a variety of coloring problems for plane graphs, involving vertices, edges, and faces in all possible combinations. For instance, in the \emph{entire coloring} of a plane graph we are to color these three sets so that any pair of adjacent or incident elements get different colors.
Jarosław Grytczuk +2 more
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On the Laplacian spectral radii of Halin graphs
Journal of Inequalities and Applications, 2017 Let T be a tree with at least four vertices, none of which has degree 2, embedded in the plane. A Halin graph is a plane graph constructed by connecting the leaves of T into a cycle. Thus the cycle C forms the outer face of the Halin graph, with the tree
Huicai Jia, Jie Xue
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The Degree Distribution of Thickened Trees [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We develop a combinatorial structure to serve as model of random real world networks. Starting with plane oriented recursive trees we substitute the nodes by more complex graphs.
Michael Drmota +2 more
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Weight of 3-Paths in Sparse Plane Graphs
Electronic Journal of Combinatorics, 2015 We prove precise upper bounds for the minimum weight of a path on three vertices in several natural classes of plane graphs with minimum degree 2 and girth $g$ from 5 to 7. In particular, we disprove a conjecture by S. Jendrol' and M. Macekova concerning
V. Aksenov, O. Borodin, A. Ivanova
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Aequationes Mathematicae, 1975 The orthogonality relation among subspaces of a finite vector space is studied here by means of the corresponding graph. In the case we consider, this graph has some highly symmetric induced subgraphs. We find three infinite families of graphs of girth 3, and two infinite families of graphs of girth 5, whose automorphism groups are transitive on ...
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Nonlocal Minimal Graphs in the Plane are Generically Sticky [PDF]
, 2019 We prove that nonlocal minimal graphs in the plane exhibit generically stickiness effects and boundary discontinuities. More precisely, we show that if a nonlocal minimal graph in a slab is continuous up to the boundary, then arbitrarily small ...
S. Dipierro, O. Savin, E. Valdinoci
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Minimal unavoidable sets of cycles in plane graphs [PDF]
Opuscula Mathematica, 2018 A set \(S\) of cycles is minimal unavoidable in a graph family \(\cal{G}\) if each graph \(G \in \cal{G}\) contains a cycle from \(S\) and, for each proper subset \(S^{\prime}\subset S\), there exists an infinite subfamily \(\cal{G}^{\prime}\subseteq\cal{
Tomáš Madaras, Martina Tamášová
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