Let us consider a figure of the Euclidean plane comprised of finitely many non-degenerate non-overlapping triangles (i.e., no triangle has a zero area and no two distinct triangles have any inner point in common).
Two distinct triangles are said to be neighbors iff they have at least two points in common (i.e., they share a portion of side of non-zero length, so indeed infinitely many points).
Must there be at least one triangle that has at most three neighbors?
Is this a known problem?
Thanks in advance.