Results 11 to 20 of about 69,266 (252)
Straight line embeddings of cubic planar graphs with integer edge lengths [PDF]
Journal of Graph Theory, 2008 AbstractUnder what conditions is it true that if there is a graph homomorphism G □ H → G □ T, then there is a graph homomorphism H→ T? Let G be a connected graph of odd girth 2k + 1. We say that G is (2k + 1)‐angulated if every two vertices of G are joined by a path each of whose edges lies on some (2k + 1)‐cycle.
Jim Geelen, Anjie Guo, David McKinnon
semanticscholar +14 more sources
On the Number of Acute Triangles in a Straight-Line Embedding of a Maximal Planar Graph
Journal of Combinatorial Theory, Series B, 1999 We show that any maximal planar graph with \(m\) triangles except the unbounded face can be transformed into a straight-line embedding in which at least \(\lceil m/3\rceil\) triangles are acute triangles. Moreover, we show that any maximal outer-planar graph can be transformed into a straight-line embedding in which all faces are acute triangles except
Atsushi Kaneko +2 more
semanticscholar +4 more sources
Straight-Line Grid Drawings of 3-Connected 1-Planar Graphs [PDF]
International Symposium Graph Drawing and Network Visualization, 2013 A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. In general, 1-planar graphs do not admit straight-line drawings. We show that every 3-connected 1-planar graph has a straight-line drawing on an integer grid of quadratic size, with the exception of a single edge on the outer face that has one bend.
Md. Jawaherul Alam +2 more
semanticscholar +4 more sources
An exact algorithm for disaster-resilience augmentation of planar straight-line graphs
Journal of Global OptimizationAbstract We consider the problem of adding a minimum length set of edges to a geometric graph so that the resultant graph is resilient against partition from the effect of a single disaster. Disasters are modeled by discs of given maximum radius, and a disaster destroys all edges intersecting its interior.
Alexander Westcott, Charl Ras
semanticscholar +3 more sources
Augmenting Planar Straight Line Graphs to 2-Edge-Connectivity
International Symposium Graph Drawing and Network Visualization, 2015 We show that every planar straight line graph PSLG with n vertices can be augmented to a 2-edge-connected PSLG with the addition of at most $$\lfloor 4n-4/3\rfloor $$ new edges. This bound is the best possible.
Hugo A. Akitaya +4 more
semanticscholar +4 more sources
A Linear Time Algorithm for Constructing Maximally Symmetric Straight-Line Drawings of Planar Graphs [PDF]
International Symposium Graph Drawing and Network Visualization, 2005 This paper presents a linear time algorithm for constructing maximally symmetric straight-line drawings of biconnected and one-connected planar graphs.
Seok-Hee Hong, Peter Eades
semanticscholar +4 more sources
O( n log log n )-work parallel algorithms for straight-line grid embeddings of planar graphs [PDF]
Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures, 1992 Martin Fürer +3 more
semanticscholar +4 more sources
From Tutte to Floater and Gotsman: On the Resolution of Planar Straight-line Drawings and Morphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 The algorithm of Tutte for constructing convex planar straight-line drawings and the algorithm of Floater and Gotsman for constructing planar straight-line morphs are among the most popular graph drawing algorithms.
Giuseppe Di Battista, Fabrizio Frati
doaj +3 more sources
Area-efficient planar straight-line drawings of outerplanar graphs
Discrete Applied Mathematics, 2007 AbstractIt is important to minimize the area of a drawing of a graph, so that the drawing can fit in a small drawing-space. It is well-known that a planar graph with n vertices admits a planar straight-line grid drawing with O(n2) area [H. de Fraysseix, J. Pach, R.
Ashim Garg, Adrian Rusu
openalex +3 more sources
On a Class of Planar Graphs with Straight-Line Grid Drawings on Linear Area
Journal of Graph Algorithms and Applications, 2009 A straight-line grid drawing of a planar graph G is a drawing of G on an integer grid such that each vertex is drawn as a grid point and each edge is drawn as a straight-line segment without edge crossings. It is well known that a planar graph of n vertices admits a straight-line grid drawing on a grid of area O(n).
Md. Rezaul Karim, Md. Saidur Rahman
openalex +2 more sources