Every branch of mathematics employs some notion of a product that enables the com-
bination or decomposition of its elemental structures. In graph theory there are four main …

Define the middle layer graph as the graph whose vertex set consists of all bitstrings of
length that have exactly or entries equal to 1, with an edge between any two vertices for …

For integers k≥ 1 and n≥ 2 k+ 1 the Kneser graph K (n; k) has as vertices all k-element
subsets of [n]:={1; 2;:::; n} and an edge between any two vertices (= sets) that are disjoint …

For any integer n≥ 1 a middle levels Gray code is a cyclic listing of all n-element and (n+ 1)-
element subsets of {1, 2,…, 2n+ 1} such that any two consecutive subsets differ in adding or …

The well-known middle levels conjecture asserts that for every integer n≧1, all binary
strings of length 2 (n+ 1) with exactly n+ 1 many 0s and 1s can be ordered cyclically so that …