On primitive 3-smooth partitions of .
On Principal Graphs and Weak Duality.
On problems related to characteristic vertices of graphs
On products of binary relational structures
On Projective Plane of Order 13 with a Frobenius Group of Order 39 as a Collineation Group
One of the most outstanding problems in combinatorial mathematics and geometry is the problem of existence of finite projective planes whose order is not a prime power.
On Projective Planes of Type (5, m).
On properties of a graph that depend on its distance function
If is a connected graph with distance function , then by a step in is meant an ordered triple of vertices of such that and . A characterization of the set of all steps in a connected graph was published by the present author in 1997. In Section 1 of this paper, a new and shorter proof of that characterization is presented. A stronger result for a certain type of connected graphs is proved in Section 2.
On properties of maximal 1-planar graphs
A graph is called 1-planar if there exists a drawing in the plane so that each edge contains at most one crossing. We study maximal 1-planar graphs from the point of view of properties of their diagrams, local structure and hamiltonicity.
On Property B and on Steiner Systems.
On -analogs of recursions for the number of involutions and prime order elements in symmetric groups.
On -clan geometry, .
On q-Euler numbers, q-Salié numbers and q-Carlitz numbers
On quasistars in -cubes
On -extendability of the hypercube
A graph having a perfect matching is called -extendable if every matching of size can be extended to a perfect matching. It is proved that in the hypercube , a matching with can be extended to a perfect matching if and only if it does not saturate the neighbourhood of any unsaturated vertex. In particular, is -extendable for every with
On radially extremal digraphs
We define digraphs minimal, critical, and maximal by three types of radii. Some of these classes are completely characterized, while for the others it is shown that they are large in terms of induced subgraphs.
On radially extremal graphs and digraphs, a survey
The paper gives an overview of results for radially minimal, critical, maximal and stable graphs and digraphs.
On rainbow arithmetic progressions.
On rainbow connection.
On rainbow solutions to an equation with a quadratic term.
On rainbow trees and cycles.