Every finite graph admits a simple (topological) drawing, that is, a drawing where every pair of edges intersects in at most one point. However, in combination with other restrictions simple drawings do not universally exist. For instance, kplanar graphs are those graphs that can be drawn so that every edge has at most k crossings (i.e., they admit a kplane drawing). It is known that for k≤3 , every kplanar graph admits a kplane simple drawing. But for k≥4 , there exist kplanar graphs that do not admit a kplane simple drawing. Answering a question by Schaefer, we show that there exists a function Open image in new window such that every kplanar graph admits an f(k)plane simple drawing, for all Open image in new window. Note that the function f depends on k only and is independent of the size of the graph. Furthermore, we develop an algorithm to show that every 4planar graph admits an 8plane simple drawing.
The Turing Test for Graph Drawing Algorithms
Do algorithms for drawing graphs pass theTuringTest?That is, are their outputs indistinguishable from graphs drawn by humans? We address this question through a humancentred experiment, focusing on ‘small’ graphs, of a size for which it would be reasonable for someone to choose to draw the graph manually. Overall, we find that handdrawn layouts can be distinguished from those generated by graph drawing algorithms, although this is not always the case for graphs drawn by force directed or multidimensional scaling algorithms, making these good candidates for Turing Test success. We show that, in general, handdrawn graphs are judged to be of higher quality than automatically generated ones, although this result varies with graph size and algorithm.
 Award ID(s):
 1839274
 Publication Date:
 NSFPAR ID:
 10179486
 Journal Name:
 28th International Symposium on Graph Drawing and Network Visualization (GD)
 Sponsoring Org:
 National Science Foundation
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