Fans and Bundles in the Graph of Pairwise Sums and Products
Fans and Bundles in the Graph of Pairwise Sums and Products
Let $G^{\times}_{+}$ be the graph on the vertex-set the positive integers ${\Bbb{N}}$, with $n$ joined to $m$ if $n\neq m$ and for some $x,y\in{\Bbb{N}}$ we have $x+y=n$ and $x\cdot y=m$. A pair of triangles sharing an edge (i.e., a $K_4$ with an edge deleted) and containing three consecutive numbers is …