A subset U of a set S with a binary operation is called avoidable if S can be partitioned into two subsets A and B such that no element of U can be written as a product of two dis...
For each integer m 1, consider the graph Gm whose vertex set is the set N = {0, 1, 2, . . . } of natural numbers and whose edges are the pairs xy with y = x + m or y = x - m or y...
In [Kit1] Kitaev discussed simultaneous avoidance of two 3-patterns with no internal dashes, that is, where the patterns correspond to contiguous subwords in a permutation. In thre...
We investigate the supereulerian graph problems within planar graphs, and we prove that if a 2-edge-connected planar graph G is at most three edges short of having two edge-disjoi...
We prove several results dealing with various counting functions for partitions of an integer into four squares of equal parity. Some are easy consequences of earlier work, but tw...
A class of graphs called generalized ladder graphs is defined. A sufficient condition for pairs of these graphs to be chromatically equivalent is proven. In addition a formula for...
We look at binary strings of length n which contain no odd run of zeros and express the total number of such strings, the number of zeros, the number of ones, the total number of ...