Results 51 to 60 of about 196,625 (294)
Contact Representations of Graphs in 3D
, 2015 We study contact representations of graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We show that for every 3-connected planar graph, there
A Bezdek +17 more
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1-planarity of complete multipartite graphs
Discrete Applied Mathematics, 2012 AbstractA graph is called 1-planar if there exists its drawing in the plane such that each edge is crossed at most once. We present the full characterization of 1-planar complete k-partite graphs.
Dávid Hudák, Július Czap
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Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends
, 2018 We study the following classes of beyond-planar graphs: 1-planar, IC-planar, and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar, and NIC-planar drawing, respectively.
C Bachmaier +13 more
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On An Extremal Problem In The Class Of Bipartite 1-Planar Graphs
Discussiones Mathematicae Graph Theory, 2016 A graph G = (V, E) is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. In this paper, we study bipartite 1-planar graphs with prescribed numbers of vertices in partite sets.
Czap Július +2 more
doaj +1 more source
Equitable Coloring and Equitable Choosability of Planar Graphs without chordal 4- and 6-Cycles [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 A graph $G$ is equitably $k$-choosable if, for any given $k$-uniform list assignment $L$, $G$ is $L$-colorable and each color appears on at most $\lceil\frac{|V(G)|}{k}\rceil$ vertices.
Aijun Dong, Jianliang Wu
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Planar Graphs of Maximum Degree 6 and without Adjacent 8-Cycles Are 6-Edge-Colorable
Journal of Mathematics, 2021 In this paper, by applying the discharging method, we show that if G is a planar graph with a maximum degree of Δ=6 that does not contain any adjacent 8-cycles, then G is of class 1.
Wenwen Zhang
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Bar 1-Visibility Drawings of 1-Planar Graphs
, 2013 A bar 1-visibility drawing of a graph $G$ is a drawing of $G$ where each vertex is drawn as a horizontal line segment called a bar, each edge is drawn as a vertical line segment where the vertical line segment representing an edge must connect the ...
A.M. Dean +13 more
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On RAC drawings of 1-planar graphs
Theoretical Computer Science, 2017 Abstract A drawing of a graph is 1-planar if each edge is crossed at most once. A graph is 1-planar if it has a 1-planar drawing. A k-bend RAC (Right Angle Crossing) drawing of a graph is a polyline drawing where each edge has at most k bends and edges cross only at right angles. A graph is k-bend RAC if it has a k -bend RAC drawing.
Bekos, Michael A. +4 more
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The Associations Between Chronic Active Lesions and White Matter Disease: A 7 Tesla Imaging Study
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Background The relationship between paramagnetic rim lesions (PRLs) and surrounding normally appearing white matter (NAWM) disease, potentially contributory to the associations seen between PRLs and clinical impairment, is underexplored. Objectives To assess whether PRLs correlate with a greater degree of NAWM injury in early MS.
Ellie McCluey +17 more
wiley +1 more source
Precise Upper Bound for the Strong Edge Chromatic Number of Sparse Planar Graphs
Discussiones Mathematicae Graph Theory, 2013 We prove that every planar graph with maximum degree ∆ is strong edge (2∆−1)-colorable if its girth is at least 40+1. The bound 2∆−1 is reached at any graph that has two adjacent vertices of degree ∆.
Borodin Oleg V., Ivanova Anna O.
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