  The pressing game on black-and-white graphs is the following: Given a graph
$G(V,E)$ with its vertices colored with black and white, any black vertex $v$
can be pressed, which has the following effect: (a) all neighbors of $v$ change
color, i.e. white neighbors become black and \emph{vice versa}, (b) all pairs
of neighbors of $v$ change connectivity, i.e. connected pairs become
unconnected, unconnected ones become connected, (c) and finally, $v$ becomes a
separated white vertex. The aim of the game is to transform $G$ into an all
white, empty graph. It is a known result that the all white empty graph is
reachable in the pressing game if each component of $G$ contains at least one
black vertex, and for a fixed graph, any successful transformation has the same
number of pressed vertices.
  The pressing game conjecture is that any successful pressing path can be
transformed into any other successful pressing path with small alterations.
Here we prove the conjecture for linear graphs. The connection to genome
rearrangement and sorting signed permutations with reversals is also discussed.
