In Graph Theory it can refer to a number of things:
i) total colouring conjecture - which holds for bipartite and planar graphs
ii)list colouring conjecture - type of colouring
iii) Dinitz conjecture - something to do with lattin squares
iv) Reconstruction conjecture - i.e. graps are determined by their subgraphs
I'm sure there are others - its been a while....