By Jiří Matoušek (auth.), Jan Kratochvíyl (eds.)
This ebook constitutes the completely refereed post-proceedings of the seventh foreign Symposium on Graph Drawing, GD '99, held in Stirin citadel, Czech Republic, in September 1999.
The 38 revised complete papers awarded including 3 invited contributions, posters, and a record at the graph drawing contest have been conscientiously reviewed and chosen from fifty nine submissions. one of the subject matters addressed are orthogonality, degrees, clusters, drawing, planarity, functions, symmetry, representations, and proximity and bushes.
Read or Download Graph Drawing: 7th International Symposium, GD’99 à tiřín Castle, Czech Republic September 15–19, 1999 Proceedings PDF
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Additional info for Graph Drawing: 7th International Symposium, GD’99 à tiřín Castle, Czech Republic September 15–19, 1999 Proceedings
Sample text
6] Let D be a drawing of a planar connected graph G. Let f be an internal face of D. Then, deg(f, 270◦ , D) − deg(f, 90◦ , D) + 2deg(f, 360◦ ) = −4. Let G be a connected planar graph with two distinguished vertices u, and v with degree at most 2, called its poles. A polar drawing of G is one in which both u and v are on its external face (see Figure 1). Let D be a polar drawing of G with external face f . f consists of two subpaths p1 and p2 connecting u and v, which are called its contour paths.
We construct D using Algorithm LinearDraw(G) after making two modifications in it: 1. If a 3-legged cycle C contains a degree-2 vertex z, then z can be designated a corner vertex of C. This obviates the need to insert a new dummy vertex in an edge of C in Step 1 of Algorithm FeasibleDraw. We, therefore, change the definition of a green path of a 3-legged cycle C as follows: – If C does not contain any child cyle, or no child cycle of C has a green path that has an edge in common with C, then • if none of the three contour paths contain a degree-2 vertex, then all the three contour paths are categorized as green paths, otherwise • a contour path of C is categorized as a green path if and only it contains a degree-2 vertex, – if C contains at least one child cycle that has a green path that has an edge in common with C, then a contour path of C is categorized as a green path if and only if either it has an edge in common with a green path of a child cycle, or it contains a degree-2 vertex.
The graphs in the test suite have been generated with a technique used in other experimental studies on orthogonal drawings [1]. Each biconnected 4planar graph is generated from a cycle of three vertices by performing a random series of InsertVertex and InsertEdge operations. The InsertVertex operation subdivides an existing edge into two new edges separated by a new vertex. The InsertEdge operation inserts a new edge between two existing vertices on the same face. Any biconnected planar graph can be generated by a sequence of these two operations.
