An election algorithm for a network is a procedure that enables to
distinguish exactly one vertex of the network. This paper presents
a necessary and sufficient condition for a family of graphs to admit
an election algorithm. We also give a universal algorithm to proceed
an election in a given family where the condition is fulfilled.
The condition involves graphs covering and quasi-covering; the
universal election algorithm is based upon an enumeration algorithm
of Mazurkiewicz and a stable properties detection algorithm of
Szymanski, Shi and Prywes.
