M.M. Syslo, Series-parallel graphs and depth-first search trees, IEEE Transactions on Circuits and Systems, 31(12), 1029-1033, (1984).  Home/Search   Document Not in Database   Summary   Related Articles

....better than that of the algorithm itself) for the decision, in the case that the tree is not a DFS tree. Analogous results for directed graphs are also given in [KO b] A constructive proof that every spanning tree of a series parallel graph G is a DFS tree of a a 2isomorphic copy of G appears in [Sy]. 2. SOME DEFINITIONS and CONVENTIONS Let T be an undirected spanning tree in an undirected graph G = V, E) and let s V. T s is the tree T together with the orientation that makes s the root of T s . T is called a DFS tree (T DFS) in G if there exists a vertex s V such that T s is a DFS tree ....

....1 i, j 4 be the six paths between v i and v j homeomorphic to the edges of the K 4 . Let l 12 , l 23 , and l 13 be edges on p 12 , p 23 and p 13 , respectively. One can see that G l 12 , l 13 , l 23 is a spanning tree of G which is not a T DFS. # (A proof of this proposition appears also in [Sy]. Corollary 3.6: A Total DFS Graph does not contain a subgraph homeomorphic to K 4 . # Proposition 3.7: Let G be a T DFS G with at least 2 circuits, and assume that a, b V are contained in all circuits of G. Then there are three paths, pairwise internally disjoint between a and b in G. # # ....

M.M. Syslo, Series-parallel graphs and depth-first search trees, IEEE Transactions on Circuits and Systems, 31(12), 1029-1033, (1984).

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