abstract
Fans and bundles in the graph of pairwise sums and products
Lorenz Halbeisen
Let G be the graph on the vertex-set the positive integers
N, with n joined to m if n and m
are distinct and for some x,y
in N we have x+y = n and x y = m. A pair of
triangles sharing an edge and containing three consecutive
numbers is called a 2-fan, and three triangles on 5 numbers
having one number in common and containing four consecutive numbers is
called a 3-fan. It will be shown that G contains 3-fans,
infinitely many 2-fans and even arbitrarily large bundles of
triangles sharing an edge. Finally, it will be shown that the
chromatic number of G is at least 4.