Let A be a finite set. A partial clone on A is a set of partial functions closed under composition and containing all projection functions on A. We survey some results in the theory of partial clones. In particular,
1- we show the link between The Erdös-Faber-Lovsáz conjecture for graphs and combinatorial descriptions of some maximal partial clones,
2- we give a complete classification of certain intervals of partial clones, that solves an open problem by D. Lau.
These results were obtain in collaboration with C. Tardif (1) and M. Couceiro, K. Schölzel and T. Waldhauser (2).