The D'Esopo-Pape algorithm is exponential in the worst case. Consider the following method to construct pathological graphs of $n$ vertices (Kershenbaum 1981), each vertex identified by a number $1, \ldots, n$ :
KershenbaumAlgorithm( )
construct a two-vertex graph with vertices 1 and 2 , and edge $(1,2)=1$;
for $(k=3 ; k<=n ; k++)$
add vertex $\mathrm{k}$;
for $(i=2 ; i<k ; i++)$
add edge $(k, i)$ with weight $(\operatorname{edge}(k, i))=\operatorname{weight}(\operatorname{edge}(1, i))$;
weight $($ edge $(1, \mathrm{i}))=$ weight $(1, \mathrm{i})+2^{\mathrm{k}-3}+1 ;$
add edge $(1, \mathrm{k})$ with weight $(\operatorname{edge}(1, \mathrm{k}))=1$;
The vertices adjacent to vertex 1 are put in ascending order and the remaining adjacency lists are in descending order. Using this algorithm, construct a five-vertex graph and execute the D'Esopo-Pape algorithm showing all changes in the deque and all edge updates. What generalization can you make about applying Pape's method to such graphs?