Results 11 to 20 of about 107,869,965 (249)
The Stub Resolution of 1-planar Graphs
Journal of Graph Algorithms and Applications, 2021 The resolution of a drawing plays a crucial role when defining criteria for its quality. In the past, grid resolution, edge-length resolution, angular resolution and crossing resolution have been investigated.
Michael Kaufmann +5 more
doaj +2 more sources
Drawing Outer 1-planar Graphs with Few Slopes [PDF]
Journal of Graph Algorithms and Applications, 2015 A graph is outer 1-planar if it admits a drawing where each vertex is on the outer face and each edge is crossed by at most another edge. Outer 1-planar graphs are a superclass of the outerplanar graphs and a subclass of the planar partial 3-trees.
Emilio Di Giacomo +2 more
doaj +2 more sources
Upward Embeddings and Orientations of Undirected Planar Graphs
Journal of Graph Algorithms and Applications, 2003 An upward embedding of an embedded planar graph specifies, for each vertex v, which edges are incident on v "above" or "below" and, in turn, induces an upward orientation of the edges from bottom to top.
Walter Didimo, Maurizio Pizzonia
doaj +2 more sources
k-L(2, 1)-labelling for planar graphs is NP-complete for k>=4 [PDF]
, 2009 A mapping from the vertex set of a graph G=(V,E) into an interval of integers {0,...,k} is an L(2,1)-labelling of G of span k if any two adjacent vertices are mapped onto integers that are at least 2 apart, and every two vertices with a common ...
Noble, Steven +8 more
core +5 more sources
Good triangulations yield good tours [PDF]
, 2008 Consider the following heuristic for planar Euclidean instances of the Traveling Salesman Problem (TSP): select a subset of the edges which induces a planar graph, and solve either the TSP or its graphical relaxation on that graph. In this paper, we give
Pearson, N, Letchford, A N
core +5 more sources
The nonsolvability by radicals of generic 3-connected planar Laman graphs. [PDF]
, 2007 We show that planar embeddable -connected Laman graphs are generically non-soluble. A Laman graph represents a configuration of points on the Euclidean plane with just enough distance specifications between them to ensure rigidity.
Power, Stephen C., Owen, J. C.
core +4 more sources
Exploiting planarity in separation routines for the symmetric traveling salesman problem [PDF]
, 2008 At present, the most successful approach for solving large-scale instances of the Symmetric Traveling Salesman Problem to optimality is branch-and-cut.
Adam N. Letchford +5 more
core +5 more sources
, 2013 In this paper, the concept of Total semirelib graph of a planar graph is introduced. Authors present a characterization of those graphs whose total semirelib graphs are planar, outer planar, Eulerian, hamiltonian with crossing number ...
Prasad, Manjunath +3 more
core +1 more source
Minimizing the oriented diameter of a planar graph [PDF]
, 2009 We consider the problem of minimizing the diameter of an orientation of a planar graph. A result of Chvátal and Thomassen shows that for general graphs, it is NP-complete to decide whether a graph can be oriented so that its diameter is at most two.
Noble, SD +3 more
core +1 more source
The Liouville and the intersection properties are equivalent for planar graphs [PDF]
, 2012 It is shown that if a planar graph admits no non-constant bounded harmonic function then the trajectories of two independent simple random walks intersect almost ...
Itai Benjamini +5 more
core +1 more source