IR-MO 2008 Problem 7

A graph is called a self-intersectinggraph if it is isomorphic to a graph whose every edge is a segment and every two edges intersect. Notice that no edge contains a vertex except its two endings. a) Find all $n$ 's for which the cycle of length $n$ is self-intersecting. b) Prove that in a self-intersecting graph $|E(G)|\leq|V(G)|$ . c) Find all self-intersecting graphs.