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Publications

last updated: November 12, 2011

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Order of presentation of publications:

  1. Refereed journals
  2. Refereed conference proceedings
  3. Invited talks
  4. Other conference presentations
  5. Deposited preprints
  6. Popular publications
  7. Other non-peer reviewed material (technical reports, etc.) are not listed
Refereed journals
  1. [1] S. Lawrencenko, [pdf] Polyhedral suspensions of arbitrary genus, Graphs & Combinatorics 26 (2010), 537—548.

  1.    

    Abstract: A new class of polyhedra is discovered—bipyramids of arbitrarily prescribed genus. A two-dimensional generalization of Fary's Theorem is established. A purely combinatorial definition of a polyhedral suspension is given. A new regular two-dimensional polyhedron is constructed in four dimensions.

  1. [2] S. Lawrencenko, M. D. Plummer, X. Zha, Isoperimetric constants of infinite plane graphs, Discrete & Computational Geometry 28 (2002), no. 3, 313—330.
  2. [3] S. Lawrencenko, S. Negami, I. Kh. Sabitov, [pdf] A simpler construction of volume polynomials for a polyhedron, Beiträge zur Algebra und Geometrie (Contributions to Algebra and Geometry) 43 (2002), no 1, 261—273.
  3. [4] S. Lawrencenko, M. D. Plumer, X. Zha, Bounds for isoperimetric constants of infinite plane graphs, Discrete Applied Mathematics 113 (2001), no. 2—3, 237—241.
  4. [5] B. Chen, J. H. Kwak, S. Lawrencenko, [pdf] Weinberg bounds over nonsperical graphs, Journal of Graph Theory 33 (2000), no. 4, 220—236.
  5. [6] B. Chen, S. Lawrencenko, A note on cyclic colorations and minimal triangulations, Yokohama Mathematical Journal 47 (1999), 93—99.
  6. [7] S. Lawrencenko, S. Negami, [pdf] Constructing the graphs that triangulate both the torus and the Klein bottle, Journal of Combinatorial Theory, Series B 77 (1999), no. 1, 211—218.
  7. [8] S. Lawrencenko, J. Mao, C. Wang, On the uniqueness of embedding a graph into a surface, Mathematica Applicata 11 (1998), no. 2, 86—89.
  8. [9] B. Chen, S. Lawrencenko, [pdf] Structural characterization of projective flexibility, Discrete Mathematics 188 (1998), no. 1—3, 233—238.
  9. [10] S. Lawrencenko, Q. Luo, [pdf] Graphs with given connectivity properties, Networks 30 (1997), no. 4, 255—261.
  10. [11] S. Lawrencenko, J. Mao, [pdf] A sharp lower bound for the number of connectivity-redundant nodes, Ars Combinatoria 47 (1997), 255—262.
  11. [12] S. Lawrencenko, S. Negami, [pdf] Irreducible triangulations of the Klein bottle, Journal of Combinatorial Theory, Series B 70 (1997), no. 2, 265—291.
  12. [13] S. Lawrencenko, S. Negami, A. T. White, [pdf] Three nonisomorphic triangulations of an orientable surface with the same complete graph, Discrete Mathematics 135 (1994), no. 1—3, 367—369.
  13. [14] F. Harary, S. Lawrencenko, V. Korzhik, Realizing the chromatic numbers of triangulations of surfaces, Discrete Mathematics 122 (1993), no. 1—3, 197—204.
  14. [15] S. Lawrencenko, The variety of triangular embeddings of a graph in the projective plane, Journal of Combinatorial Theory, Series B 54 (1992), no. 2, 196—208.
  15. [16] S. A. Lavrenchenko, Number of triangular packings of a marked graph on a projective plane, Journal of Methematical Sciences 59 (1992), no. 2, 741—749.
  16. [17] S. Lawrencenko, On the number of triangular embeddings of a labeled graph in the projective plane [in Russian], Ukrainskii Geometricheskii Sbornik (Ukrainian Geometry Collection) No. 32 (1989), 71—84.
  17. [18] S. A. Lavrenchenko, The number of triangular packings of a vertex labeled graph on a torus, Journal of Mathematical Sciences 54 (1991), no. 1, 719—728.
  18. [19] S. Lawrencenko, On the number of triangular embeddings of a vertex-labeled graph in the torus [in Russian], Ukrainskii Geometricheskii Sbornik (Ukrainian Geometry Collection) No. 31 (1988), 76—90.
  19. [20] S. A. Lavrenchenko, [pdf] Irreducible triangulations of the torus, Journal of Mathematical Sciences 51 (1990), no. 5, 2537—2543.
  20. [21] S. Lavrenchenko, An infinite set of torus triangulations of connectivity 5 whose graphs are not uniquely embeddable in the torus, Discrete Mathematics 66, no. 3, 299—301.
  21. [22] S. Lawrencenko, [pdf] Irreducible triangulations of the torus [in Russian], Ukrainskii Geometricheskii Sbornik (Ukrainian Geometry Collection) No. 30 (1987), 52—62.
Refereed conference proceedings
  1. [23] S. Lawrencenko, Construction of quadrangulations of surfaces with prescribed properties, In CET'11: Proceedings of 2011 World Congress on Engineering and Technology, Vol. 02, pp. 121—125, Beijing: IEEE Press, 2011. ISBN 978-1-61284-362-9.
  1. Abstract. A class of “spinal” quadrangulations of closed orientable surfaces is constructed. The properties of such quadrangulations are predetermined by their spines; especially, the genus g of a spinal quadrangulation of the sphere with g handles is equal to the 1st Betti number of its spine. A method is developed for generating quadrangulations with prescribed properties by way of spinal manipulation. Many new minimal quadrangulations with given genus are found. The following homology lemma is used: given a 1- or 2-dimensional topological (curved) polyhedron P in Euclidean 3-space, the boundary of a small 3-dimensional neighborhood of P is a closed orientable surface whose total number of handles is equal to the 1st Betti number of P and whose total number of connected components is equal to the sum of the 0th and 2nd Betti numbers of P.

  1. [24] A. V. Betin, S. A. Lawrencenko, A graph theoretical approach to a pharmaceutical problem [in Russian]. In A. P. Kudinov and B. V. Krylov, eds., PhysioMedi, Proceedings of 2nd International Scientific and Practical Conference "High-Tech, Fundamental and Applied Research in Physiology and Medicine", Vol. 2, pp. 123—125, St. Peterburg: Polytech. Univ. Publishing, 2011. ISBN 978-5-7422-3209-4.
  2. [25] S. Lawrencenko, Construction of quadrangulations of surfaces with given properties [in Russian], In Yu. I. Zhuravlev, ed., Problems of Theoretical Cybernetics. Proceedings of XVI International Conference, pp. 259—263, Nizhny Novgorod: Nizhny Novgorod State Univ. Publishing, 2011. ISBN 978-5-91326-161-8.
  3. [26] S. Lawrencenko, A new regular polyhedron [in Russian]. In O. M. Kasim-Zade, ed., Proceedings of X International Seminar "Discrete Mathematics and Its Applications", pp. 495—498, Moscow: Moscow State Univ. MechMath Publishing, 2010.
  4. [27] S. Lawrencenko, Three approaches to the concept of a reliable connection in communication networks [in Russian]. In ICEEE-2003: Proceedings of 5th International Conference on Electromechanics, Electrotechnology and Electromaterial Science, Part II, pp. 354—357, Moscow: Moscow Power Eng. Inst. Publishing. 2003.
  5. [28] S. Lawrencenko, X. Liu, Y. Liu, An algorithm for constructing a rectilinear embedding of a given graph in the plane. In Combinatorics and Graph Theory, Vol. 1, pp. 205—217, River Edge, NJ: World Sci. Publishing, 1995.
Invited talks
  1. [29] S. Lawrencenko, Generalized polyhedral suspensions. Invited talk at Yokohama National University, 20th Workshop on Topological Graph Theory in Yokohama. November, 2008.
  2. [30] S. Lawrencenko, Minimal triangulations and cyclic colorations. Invited talk at Yokohama National University, 10th Workshop on Topological Graph Theory in Yokohama. November, 1998.
  3. [31] S. Lawrencenko, Infinite regular toroidal triangulations. Invited talk at Yokohama National University, 4th Workshop on Topological Graph Theory in Yokohama. November, 1992.
Other conference presentations
  1. [32] S. Lawrencenko, On an interesting surface associated with a given polyhedron [in Russian]. In G. N. Zholtkevich, N. N. Kizilova, P. S. Kabalyants, eds., Contemporary Problems of Mathematics and Its Application in Natural Sciences and Information Technologies. Abstracts of the International Conference (Apr. 17—22, 2011, Kharkov, Ukraine), p. 146, Kharkov: Virovets A. P. "Apostrophe", 2011.
  2. [33] S. Lawrencenko and N. Sanders, Generalized polyhedral suspensions. The 20th Workshop on Topological Graph Theory in Yokohama (Nov. 25—28, 2008, Yokohama, Japan). Abstracts, pp. 92—101, Yokohama: Yokohama Publishers, 2008.
  3. [34] S. Lawrencenko and O. Bose, A note on g-outer graphs. Thirty-Second Southeastern International Conference on Combinatorics, Graph Theory and Computing (Feb. 26— Mar. 2, 2001), Baton Rouge, Louisiana, USA). Abstracts, p. 22.
  4. [35] S. Lawrencenko and N. Sanders, Bipyramids of arbitrary genus. Thirty-Second Southeastern International Conference n Combinatorics, Graph Theory, and Computing (Feb. 26— Mar. 2, 2001, Baton Rouge, Louisiana, USA). Abstracts, p. 128.
  5. [36] S. Lawrencenko and M. D. Plummer, Irreducible triangulations of pseudosurfaces, Joint Mathematics Meetings, (Jan. 19—22, 2000, Washington, DC, USA), Notices of the AMS 47 (2000), no. 1, p. 165.
  6. [37] S. Lawrencenko, Flexibility of maps on surfaces, First Pacific Rim Conference on Mathematics (Jan. 19—23, 1998, Hong Kong, China). Abstracts, p. 35—36.
  7. [38] S. Lawrencenko, On the maximum order of the automorphism group of a fixed-genus graph, Fourth Czechoslovakian Symposium on Combinatorics (1990, Prachatice, Czechoslovakia), Abstracts, p. 43.
  8. [39] S. Lawrencenko, Every 6-connected toroidal graph in Hamiltonian [in Russian]. In O. B. Lupanov, ed., Proceedings of Workshop on Discrete Mathematics and Its Applications, p. 281, Moscow State Univ. Publishing, Moscow, 1989.
  9. [40] S. Lawrencenko, Description of the family of graph triangularly embeddable on both the torus and the Klein bottle [in Russian]. In Yu. G. Reshetnyak, ed., All-Union Conference on Geometry in the Large (Sept. 28—30, 1987, Novosibirsk, USSR), Abstracts, p. 68, Novosibirsk: AS USSR Siberian Branch Inst. Math Publishing, 1987.
  10. [41] S. A. Lavrenchenko, All self-complementary simplicial 2-complexes homeomorphic to the torus or the projective plane, Baku International Topological Conference (Oct. 3—9, 1987, Baku, Azerbaijan). Abstracts (part II), p. 159, Baku, 1987.
  11. [42] S. Lawrencenko, On the number of triangular embeddings of a labeled graph on a 2-manifold [in Russian]. In Joint Enlarged Sessions of the Seminar on Geometry in the Large and the Scientific Seminar of Department of Mathematical Analysis Dedicated to the 75th anniversary of N. V. Efimov. Abstracts, Vestnik Moskovskogo Universiteta — Math and Mech. (Bulletin of Moscow University — Math and Mech.), 5 (1986), 96—97.
Deposited preprints
  1. [43] S. Lawrencenko and M. N. Ellingham, Characterization of flexible 2-complexes with a few vertices, AIM Reprint Library, 2000, vol. 1, color: orange, original reprint.
  2. [44] S. Lawrencenko, Tables of all essentially different triangulations of the projective plane with some interesting graphs [in Russian], Preprint deposited at VINITI, No. 613-V89, Moscow, 1989, 23 p.
  3. [45] S. Lawrencenko, Explicit enumeration of all automorphisms of the irreducible triangulations of the torus, and all torus embeddings of the labeled graphs of these triangualations [in Russian], Preprint deposited at UkrNIINTI, No. 2779-Uk87, Kharkov, 1987, 57 p.
Popular publications
  1. [46] A. V. Bushmelev and S. Lawrencenko, Polyhedral tori [in Russian], Kvant 2 (1985), 3—5.
Other non-peer reviewed material (technical reports, etc.)
  1. are not listed.
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