"Subpaths" of Dijkstra's shortest path also shortest? I have trouble putting this into formal mathematical terms, so let's suppose that I found the shortest path from A to E as A > C > D > B > F > E with Dijkstra's algorithm. Am I correct in assuming that the shortest path from C to B would be C > D > B, and that the shortest path from D to F would be D > B > F?
Of course, it is true. However, it is not a property of Dijkstra's algorithm but is property of the shortest paths themselves. Suppose that is not true, and you have a shorter path from $C$ to $B$, we denote it as $p_{CB}$. Then we would have a path $A \rightarrow p_{CB} \rightarrow F \rightarrow E$ from $A$ to $E$ which is shorter than $A  \rightarrow  C  \rightarrow  D  \rightarrow B  \rightarrow  F  \rightarrow E$.