A graph is called well-covered if every maximal independent set has the same size. One generalization of independent sets in graphs is that of a fractional cover -- attach nonnegative weights to the vertices and require ...

The thesis begins by giving background in linear programming and Simplex methods. Topics covered include the duality theorem, Lemke's algorithm, and the pathological programs of Klee-Minty. Because of the bad behaviour ...

We construct infinite cubefree binary words containing exponentially many distinct squares of length n . We also show that for every positive integer n , there is a cubefree binary square of length 2n.

Given an infinite word x over an alphabet A, a letter b occurring in x, and a total order \sigma on A, we call the smallest word with respect to \sigma starting with b in the shift orbit closure of x an extremal word of ...

The critical exponent of an infinite word w is the supremum of all rational numbers α such that w contains an α-power. We resolve an open question of Krieger and Shallit by showing that for each α>2 there is an infinite ...

Richomme asked the following question: what is the infimum of the real numbers α > 2 such that there exists an infinite word that avoids α-powers but contains arbitrarily large squares beginning at every position? We resolve ...

A vertex x of a graph G resolves two vertices u and v of G if the distance from x to u does not equal the distance from x to v. A set S of vertices of G is a resolving set for G if every two distinct vertices of G are ...

In 1906 Axel Thue showed how to construct an infinite non-repetitive (or square-free) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a two-dimensional ...