  We consider a model of two (fully) compact polymer chains, coupled through an
attractive interaction. These compact chains are represented by Hamiltonian
paths (HP), and the coupling favors the existence of common bonds between the
chains. Using a ($n=0$ component) spin representation for these paths, we show
the existence of a phase transition for strong coupling (i.e. at low
temperature) towards a ``frozen'' phase where one chain is completely adsorbed
onto the other. By performing a Legendre transform, we obtain the probability
distribution of overlaps. The fraction of common bonds between two HP, i.e.
their overlap $q$, has both lower ($q_m$) and upper ($q_M$) bounds. This means
in particuliar that two HP with overlap greater than $q_M$ coincide. These
results may be of interest in (bio)polymers and in optimization problems.
