10 citations · 28 across the 13 of their papers we have counts for
14 papers
Old and new geometric polyhedra with few vertices
Serge Lawrencenko, Alex Lao
This paper deals with triangulations of the 2-torus with the vertex labeled general octahedral graph which is isomorphic to the complete four-partite graph ; it…
Determination of the 4-genus of a complete graph (with an appendix)
Serge Lawrencenko, Beifang Chen, Hui Yang
In this paper, the quadrangular genus (4-genus) of the complete graph is shown to be for orientable surfaces. This means that $K_p…
Grünbaum coloring and its generalization to arbitrary dimension
S. Lawrencenko, M. N. Vyalyi, L. V. Zgonnik
This paper is a collection of thoughts and observations, being partly a review and partly a report of current research, on recent work in various aspects of Grünbaum colorings, the…
Quadrangular embeddings of complete graphs and the Even Map Color Theorem (with details)
Wenzhong Liu, Serge Lawrencenko, Beifang Chen +5
Hartsfield and Ringel constructed orientable quadrangular embeddings of the complete graph for , and nonorientable ones for and $n\equiv 1 \pmod…
Irreducible triangulations of the once-punctured torus
S. Lawrencenko, T. Sulanke, M. T. Villar +3
A triangulation of a surface with fixed topological type is called irreducible if no edge can be contracted to a vertex while remaining in the category of simplicial complexes and…
Search algorithms for efficient logistics chains
Serge Lawrencenko, Irina A. Duborkina
Logistics networks arise whenever there is a transfer of material substance or objects (such as checked baggage on international flights) as well as energy, information, or finance…
All face 2-colorable d-angulations are Grünbaum colorable
Serge Lawrencenko, Abdulkarim M. Magomedov
A -angulation of a surface is an embedding of a 3-connected graph on that surface that divides it into -gonal faces. A -angulation is said to be Grünbaum colorable if its…
An algorithm that constructs irreducible triangulations of once-punctured surfaces
María José Chávez, Serge Lawrencenko, José Ramón Portillo +1
A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. In this work we propose an algorithm that construct…
Homology of polyhedra and quadrangulations of surfaces
Serge Lawrencenko
A new formula is obtained in algebraic topology, in terms of Betti numbers, and a new method, called the spinal method, is suggested and developed for generating quadrangulations o…
Geometric realization of toroidal quadrangulations without hidden symmetries
Serge Lawrencenko
It is shown that each quadrangulation of the 2-torus by the Cartesian product of two cycles can be geometrically realized in (Euclidean) 4-space without hidden symmetries---that is…
Irreducible triangulations of the Möbius band
María-José Chávez, Serge Lawrencenko, Antonio Quintero +1
A complete list of irreducible triangulations is identified on the Möbius band.
On the minimum order of a quadrangulation on a given closed 2-manifold
Serge Lawrencenko
A partial formula is provided to calculate the smallest number of vertices possible in a quadrangulation on the closed orientable 2-manifold of given genus. This extends the previo…
On irreducible triangulations of punctured and pinched surfaces
M. J. Chávez, S. Lawrencenko, A. Quintero +1
A triangulation of a punctured or pinched surface is irreducible if no edge can be shrunk without producing multiple edges or changing the topological type of the surface. The fini…
Realizing the chromatic numbers and orders of spinal quadrangulations of surfaces
Serge Lawrencenko
A method is suggested for construction of quadrangulations of the closed orientable surface with given genus g and either (1) with given chromatic number or (2) with given order al…