In this paper, we develop a novel solution for particle filtering on general graphs. We provide an exact solution for particle filtering on directed cycle-free graphs. The proposed approach relies on a partial-order relation in an antichain decomposition that forms a high-order Markov chain over the partitioned graph. We subsequently derive a closed-form sequential updating scheme for conditional density propagation using particle filtering on directed cycle-free graphs. We also provide an approximate solution for particle filtering on general graphs by splitting graphs with cycles into multiple directed cycle-free subgraphs. We then use the sequential updating scheme by alternating among the directed cycle-free subgraphs to obtain an estimate of the density propagation. We rely on the proposed method for particle filtering on general graphs for two video tracking applications: 1) object tracking using high-order Markov chains; and 2) distributed multiple object tracking based on multi-object graphical interaction models. Experimental results demonstrate the improved performance of the proposed approach to particle filtering on graphs compared with existing methods for video tracking.