Geodesic
Evolutionarily-fragmented algorithm for finding a~maximal flat part of a~graph
Prikladnaâ diskretnaâ matematika, no. 3 (2015), pp. 74-82.

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The problem of finding a maximal flat part of a separable undirected graph is considered. It is shown that this problem can be represented as an optimization problem on a fragmented structure. An evolutionary-fragmented algorithm for finding approximate solutions of the problem is proposed.
Keywords: graph, maximally flat part of graph, isometric cycles, fragmented structure, evolutionarily-fragmented algorithm. 
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I. V. Kozin; S. V. Kurapov; S. I. Poljuga. Evolutionarily-fragmented algorithm for finding a~maximal flat part of a~graph. Prikladnaâ diskretnaâ matematika, no. 3 (2015), pp. 74-82. http://geodesic.mathdoc.fr/item/PDM_2015_3_a5/

[1] Kas'yanov V. N., Evstigneev V. A., Graphs in Programming: Processing, Visualization and Application, BKhV-Peterburg Publ., St. Petersburg, 2003, 1104 pp. (in Russian)

[2] Tamassia R., Handbook of Graph Drawing and Visualization, Chapman and Hall/CRC, Boca Raton, 2013, 844 pp. | MR

[3] Kurapov S. V., Tolok A. V., “The topological drawing of a graph: Construction methods.”, Automation and Remote Control, 74:9 (2013), 1494–1509 | DOI | MR | Zbl

[4] Kurapov S. V., Davidovskiy M. V., “Two approaches to connections conducting in flat form factor”, Komponenty i tekhnologii, 2015, no. 7, 142—147 (in Russian)

[5] Garey M. R., Johnson D. S., Computers and Intractability, W. H. Freeman and Co., San Francisco, 1979, 338 pp. | MR | MR | Zbl

[6] Papadimitriou C. H. and Steiglitz K., Combinatorial Optimization. Algorithms and Complexity, Prentice-Hall, NJ, USA, 1982 | MR | MR | Zbl

[7] Harary F., Graph Theory, Addison-Wesley, 1969 | MR | MR | Zbl

[8] Swamy M. N. S., Thulasiraman K., Graphs, Networks and Algorithms, Wiley, 1980, 612 pp. | MR

[9] Zykov E. I., Basics of Graph Theory, Nauka Publ., Moscow, 1987, 384 pp. (in Russian) | MR

[10] Kurapov S. V., Pokhal'chuk T. A., “Single cycles and cuts to determine the graph isomorphism”, Vistnyk Zaporizkoho Natsionalnoho Universytetu: Zbirnyk naukovykh prats. Fz.-mat. nauky, 2011, no. 2, 61–68 (in Russian)

[11] Kurapov S. V., Savin V. V., Vector Algebra and Graph Drawing, ZDU Publ., Zaporzhzhya, 2003, 200 pp. (in Russian)

[12] Kavitha T., Liebchen C., Mehlhorn K., Michail D., et al., “Cycle bases in graphs characterization, algorithms, complexity, and applications”, Comput. Sci. Rev., 3:4 (2009), 199–243 | Zbl

[13] Kozin I. V., Polyuga S. I., “Fragmentary model for some extreme problems on graphs”, Matematychni mashyny i sistemy, 2014, no. 1, 143–150 (in Russian)

[14] Deza E. I., Deza M. M., Encyclopedic Dictionary of Distances, Nauka Publ., Moscow, 2008, 432 pp. (in Russian)

[15] Kozin I. V., Polyuga S. I., “Properties of fragmented structures”, Vistnyk Zaporizkoho Natsionalnoho Universytetu: Zbirnyk naukovykh prats. Fiz.- mat. nauky, 2012, no. 1, 99–106 (in Russian)

[16] Erdos P., Renyi A., “On random graphs. I”, Publ. Math. Debrecen, 6 (1959), 290–297 | MR | Zbl