Speciality:
01.01.09 (Discrete mathematics and mathematical cybernetics)
Phone: +7-910-458-88-82
E-mail: Website: https://lawrencenko.ru Keywords: Polyhedra, the number of topological embedding of a graph in a surface and the number of geometric polyhedra with a given 1-skeleton. The 4-genus of the complete graph. Even Map Color Theorem. Irreducible triangulations of surfaces.
UDC: 519.1, 514 MSC: 05C, 57M, 57N, 51M, 52B, 51F, 20F
Subject:
Polyhedra: Geometric realizations of abstract complexes, symmetries, discrete isoperimetric constants, volume equations for polyhedra. Mathematical modeling, flexibility of embeddings and polyhedra, triangulations of 2-, 3-, and 4-manifolds, irreducible triangulations,
coloring of graphs,
reliable networks,
spinal quadrangulations,
homology of polyhedra,
algorithms and optimization. The 4-genus of the complete graph, Even Map Color Theorem.
Main publications:
Lawrence S.A., Magomedov A.M., Chelyapina O.I. and Rudenko V.M., “Combinatorial rigidity and flexibility of simplicial 2-complexes with few vertices”, https://doi.org/10.20429/tag.2025.120102, Theory and Applications of Graphs, 12:1 (2025), Article 2.
Lawrencenko S., Lao A., “Pairs of polyhedra sharing the same 1-skeleton in 3D and 4D spaces, without a single common face”, https://doi.org/10.1080/09720529.2022.2027603, Journal of Discrete Mathematical Sciences and Cryptography, 25:1 (2022), 253–263.
Lawrencenko S., “Polyhedral suspensions of arbitrary genus”, https://doi.org/10.1007/s00373-010-0938-5, Graphs and Combinatorics, 26:4 (2010), 537–548.
Lawrencenko S., Magomedov A.M., “Generating the triangulations of the torus with the vertex-labeled complete 4-partite graph K_{2,2,2,2}”, https://doi.org/10.3390/sym13081418, Symmetry, 13:8 (2021), Paper No. 1418.
Liu W., Lawrencenko S., Chen B., Ellingham M.N., Hartsfield N., Yang H., Ye D., Zha X., “Quadrangular embeddings of complete graphs and the Even Map Color Theorem”, https://doi.org/10.1016/j.jctb.2019.02.006, Journal of Combinatorial Theory, Series B, 139 (2019), 1–26.
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