Conway's [Thrackle Conjecture][1]: $E \le V$ in any "thrackle," a particular type of drawing of a graph
of $V$ vertices and $E$ edges in the plane. Dangerously addictive!  And advances made every few years;
it is by no means an isolated conjecture.

<br />&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;![Thrackle][2]


  [1]: http://en.wikipedia.org/wiki/Conway%27s_thrackle_conjecture
  [2]: http://upload.wikimedia.org/wikipedia/en/thumb/4/44/6-cycle_thrackle.png/220px-6-cycle_thrackle.png