  An edge switch is an operation which makes a local change in a graph while
maintaining the degree of every vertex. We introduce a switch move, called a
triangle switch, which creates or deletes at least one triangle. Specifically,
a make move is a triangle switch which chooses a path $zwvxy$ of length 4 and
replaces it by a triangle $vxwv$ and an edge $yz$, while a break move performs
the reverse operation. We consider various Markov chains which perform random
triangle switches, and assume that every possible make or break move has
positive probability of being performed.
  Our first result is that any such Markov chain is irreducible on the set of
all 3-regular graphs with vertex set $\{1,2,\ldots, n\}$. For a particular,
natural Markov chain of this type,
  we obtain a non-trivial linear upper and lower bounds on the number of
triangles in the long run. These bounds are almost surely obtained in linear
time, irrespective of the starting graph.
