On a number pyramid related to the binomial, Deleham, Eulerian, MacMahon and Stirling number triangles.
On a pair of functional equations of combinatorial interest.
On a partition function of Richard Stanly.
On a perfect problem
We solve Open Problem (xvi) from Perfect Problems of Chvátal [1] available at ftp://dimacs.rutgers.edu/pub/perfect/problems.tex: Is there a class C of perfect graphs such that (a) C does not include all perfect graphs and (b) every perfect graph contains a vertex whose neighbors induce a subgraph that belongs to C? A class P is called locally reducible if there exists a proper subclass C of P such that every graph in P contains a local subgraph belonging...
On a planar construction of quasigroups
On a power of cyclically ordered sets
On a Problem About Covering Lines by Squares.
On a problem about covering lines by squares.
On a problem concerning -subdomination numbers of graphs
One of numerical invariants concerning domination in graphs is the -subdomination number of a graph . A conjecture concerning it was expressed by J. H. Hattingh, namely that for any connected graph with vertices and any with the inequality holds. This paper presents a simple counterexample which disproves this conjecture. This counterexample is the graph of the three-dimensional cube and .
On a problem concerning stratified graphs
On a Problem in Map Colouring
On a problem of colouring the real plane
What is the least number of colours which can be used to colour all points of the real Euclidean plane so that no two points which are unit distance apart have the same colour? This well known problem, open more than 25 years is studied in the paper. Some partial results and open subproblems are presented.
On a Problem of D'Atri and Nickerson.
On a problem of Davenport and Schinzel
On a problem of Davison. (Summary).
On a problem of E. Prisner concerning the biclique operator
The symbol denotes a directed graph with the vertex set for two (not necessarily disjoint) vertex sets in which an arc goes from each vertex of into each vertex of . A subdigraph of a digraph which has this form is called a bisimplex in . A biclique in is a bisimplex in which is not a proper subgraph of any other and in which and . The biclique digraph of is the digraph whose vertex set is the set of all bicliques in and in which there is an arc from into if and only...
On a problem of linear arboricity
On a problem of Marco Buratti.
On a problem of Molluzzo concerning Steinhaus triangles in finite cyclic groups.
On a problem of P. Erdös