Download e-book for iPad: (3,k)-Factor-Critical Graphs and Toughness by Shi M., Yuan X., Cai M.

By Shi M., Yuan X., Cai M.

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Additional resources for (3,k)-Factor-Critical Graphs and Toughness

Sample text

The crossing minimization problem is NP-hard even when restricted to 2-layer instances. Nevertheless, it has been attacked with a branch-and-cut algorithm that produces an optimum solution in exponential running time, see Healy and Kuusik [44]. , Elf et al. ) However, such methods have not yet reached the maturity and practical efficiency to be used in software systems for automatic graph drawing. Instead, most systems apply a layer by layer sweep as follows: Starting from some initial permutation of the vertices on each layer, such heuristics consider pairs of layers (L fixed , Lfree) = (Ll' L2), (L2' L 3 ), ...

Mannino, C. (1994) Upward drawings of triconnected digraphs. Algorithmica 6 (12), 476-497 6. , Tamassia, R. (1998) Optimal upward planarity testing of single-source digraphs. SIAM Journal on Computing 27, 132-169 7. , Lueker, G. (1976) Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences 13, 335-379 8. Brandenburg, F. , Rohrer, C. (1996) An experimental comparison of force-directed and randomized graph drawing algorithms.

A typical force-directed layout. It should be stressed that the title of this section is a concession to the short tradition of automatic graph drawing and the title "Drawing on Physical Analogies" of a recommended survey of Brandes [9] would be much more appropriate, because what follows has little to do with what physicists do when they study ground states of physical systems and relaxation dynamics. Two-Dimensional Force-Directed Layout of Undirected Graphs. For ease of notation, we identify vertices and edges with their physical counterparts.

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(3,k)-Factor-Critical Graphs and Toughness by Shi M., Yuan X., Cai M.


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