... September Meeting of the Cumann Matamaitice nah´Eireann in Cork (Ireland). Further, I would like to thank Stephanie Halbeisen for manyhints and fruitful discussions, and the referee for numerous ... colour the vertices of ˙G29with three colours x, y,andz. Without loss of generality, let us colour 14 with colourx. Since, the four numbers 13, 14, 22, and 40 form a pair of triangles sharing ... = m and for some x, y ∈ N we have x + y = n and x ·y = m . A pair of trianglessharing an edge (i.e.,aK4with an edge deleted) and containing three consecutivenumbers is called a 2-fan, and...