Let $K(x, y)$ be the number in the title. There is a function $f(r)$, concave and decreasing with $f(0) = 2$ and $f'(0) = 0$ such that if $r = \Sqrt{\log x} /\log y ...

This is a preview. Log in through your library . Abstract In a quadratic number field $\mathbf{Q}(\sqrt D), D$ a squarefree integer, with class number 1, any algebraic integer can be decomposed ...

Graph factorizations constitute a fundamental area of graph theory in which complex networks are decomposed into subgraphs, or factors, that adhere to specific properties. These factorizations not ...