  The Hammersley-Clifford theorem states that if the support of a Markov random
field has a safe symbol then it is a Gibbs state with some nearest neighbour
interaction. In this paper we generalise the theorem with an added condition
that the underlying graph is bipartite. Taking inspiration from "Gibbs Measures
and Dismantlable Graphs" by Brightwell and Winkler we introduce a notion of
folding for configuration spaces called strong config-folding proving that if
all Markov random fields supported on $X$ are Gibbs with some nearest neighbour
interaction so are Markov random fields supported on the 'strong config-folds'
and 'strong config-unfolds' of $X$.
