In 2008 we have published a scientific monograph with a respectable published of mathematical book A K Peters. The book covers topics from modern graph theory, where the topics are interconnected via the Cartesian product operation.
COBISS.SI-ID: 223132416
For a polzhedral surface S obtained from a (possibly infinite) collection of polygons, we prove that under a certain condition, S is homeomorphic to a compact 2-manifold with t points removed. In the special case when every polygon is regular and the Gaussian curvature is positive at each vertex, we apply our main theorem to deduce that R is compact and is homeomorphic to either the sphere or to the projective plane. With exception of four infinite families, |V| ( 3445. This resolves a recent conjecture of Higuchi.
COBISS.SI-ID: 14334809
In 2005 we published a paper in a prestige journal Transactions of the American Mathematical Society. The paper brings important new results about an almost duality between circular flows and circular colorings of graphs on surfaces. This presents culmination of the research of many authors and clarifies and generalizes many results previously obtained by other methods.
COBISS.SI-ID: 13781081
Circular chromatic number and circular chromatic index present one of the most important research areas in the contemporary theory of graph colorings. In this paper a fundamental theorem is proved asserting that for each epsilon ) 0 and each integer delta ) 0, there exists a number g such that for any graph G of maximum degree delta and girth at least g, the circular chromatic index of G is at most delta + epsilon.
COBISS.SI-ID: 14187353
The distinguishing number of a graph is an important graph invariant which was intensively studied in last years. We have published several papers on the topic in top journals J. Algebra, J. Graph Theory and European J. Combin. The explicitly mentioned paper has in the short period after its publication collected 9 citation according to the database MatcSciNet, which is a very big number for mathematical research.
COBISS.SI-ID: 14075225