Results 101 to 110 of about 30,213,529 (145)
On the k-Structure Ratio in Planar and Outerplanar Graphs
Discrete Mathematics & Theoretical Computer Science, 2008 A planar k-restricted structure is a simple graph whose blocks are planar and each has at most k vertices. Planar k-restricted structures are used by approximation algorithms for Maximum Weight Planar Subgraph, which motivates this work. The planar k-
Gruia Calinescu, Cristina G. Fernandes
doaj
The maximum number of edges of bipartite 1-planar graphs with 1-disk drawings
AKCE International Journal of Graphs and CombinatoricsA graph is 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. Let G be a bipartite 1-planar graph with bipartition sets X and Y. A 1-disk [Formula: see text] drawing of G is a 1-planar drawing such that all vertices
Guiping Wang
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1-Bend RAC Drawings of 1-Planar Graphs
, 2016 A graph is 1-planar if it has a drawing where each edge is crossed at most once. A drawing is RAC (Right Angle Crossing) if the edges cross only at right angles.
Mehrabi, Saeed +7 more
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Drawing Planar Graphs and 1-Planar Graphs Using Cubic Bézier Curves with Bounded Curvature [PDF]
We study algorithms for drawing planar graphs and 1-planar graphs using cubic Bézier curves with bounded curvature. We show that any n-vertex 1-planar graph has a 1-planar RAC drawing using a single cubic Bézier curve per edge, and this drawing can be ...
Goodrich, MT +5 more
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Straight-line drawings of 1-planar graphs
Computational GeometryA graph is 1-planar if it can be drawn in the plane so that each edge is crossed at most once. However, there are 1-planar graphs which do not admit a straight-line 1-planar drawing. We show that every 1-planar graph has a straight-line drawing with a two-coloring of the edges, so that edges of the same color do not cross.
openaire +2 more sources
Algorithms for graphs embeddable with few crossings per edge [PDF]
We consider graphs that can be embedded on a surface of bounded genus such that each edge has a bounded number of crossings. We prove that many optimization problems, including maximum independent set, minimum vertex cover, minimum dominating set and ...
Grigoriev,Alexander, Bodlaender,Hans
core
Parallel O(log(n)) time edge-colouring of trees and Halin graphs [PDF]
We present parallel O(log(n))-time algorithms for optimal edge colouring of trees and Halin graphs with n processors on a a parallel random access machine without write conflicts (P-RAM).
Gibbons, Alan (Alan M.) +2 more
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On randomly colouring locally sparse graphs
Discrete Mathematics & Theoretical Computer Science, 2006 We consider the problem of generating a random q-colouring of a graph G=(V,E). We consider the simple Glauber Dynamics chain. We show that if for all v ∈ V the average degree of the subgraph H v induced by the neighbours of v ∈ V is ≪Δ where Δ ...
Alan Frieze, Juan Vera
doaj
On the Independence Number of 1-Planar Graphs.
An independent set in a graph is a set of vertices where no two vertices are adjacent to each other. A maximum independent set is the largest possible independent set that can be formed within a given graph G. The cardinality of this set is referred to as the independence number of G.
Biedl, Therese +2 more
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On Radiocoloring Hierarchically Specified Planar Graphs: PSPACE-Completeness and Approximations
, 2002 Hierarchical specifications of graphs have been widely used in many important applications, such as VLSI design, parallel programming and software engineering. A well known hierarchical specification model, considered in this work, is that of Lengauer [9,
Andreou, M. +9 more
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