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I was wondering if Dijkstra’s algorithm can be modified to find the path between two nodes where the max of all the edge lengths in the path is smallest.
ie it would prefer a path of edges length 1,3,5,9 over a path of a single edge length 10 because max(1,3,5,9) < max(10)
Yes, this can be done using Dijkstra’s algorithm
Hint: At each node u, store the smallest weight w, so that there exists a path through visited vertices from s to u whose max weight is w. Think of modifying the relaxation condition upon visiting a new vertex to satisfy the above condition.