DFS Tree Construction: Algorithms and Characterizations
نویسندگان
چکیده
The Depth First Search (DF.S.) algori.thm i§. one of the basic techniques which is used in a very large variety of graph algorithms. Every -application' of the DFS involves, beside traversing the graph, cOnstructing a special structured tree, called a DFS tree. In this paper, we give a complete characterization of all the graphs in which every spanning tree is ~ 'DFS tree. These graphs are called 'Fotal-DFS -Graphs . The characterization we present·shoW~.th~t a'large variety of grap.hs are not Total-DFS-GraphS, and therefore the following Cltlestion. is naturally rais~: Giyen an undirected graph G=(V,E) 'and an undirecttd spanning tree 1=, is T a DFS tree ofG? We give' an algorithm to answer this que~tion in linear (O(IEJ)) time. An important feature-of the algorithm is that if the answer is negative then it provides a shon (0 (J V I)) proof for that fact. ·'A preliminaIy venioo of thiS worlt Willi presented allhc 14th International Worbhop on Gnph-Theorctic: Conc:cptl in Canputer Science, Amsterdam-(1988). T ec hn io n C om pu te r Sc ie nc e D ep ar tm en t T eh ni ca l R ep or t C S0 51 5 19 88
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The Depth First Search (DFS) algorithm is one of the basic techniques which is used in a very large variety of graph algorithms. Most applications of the DFS involve the construction of a depth-first spanning tree (DFS tree). In this paper, we give a complete characterization of all the graphs in which every spanning tree is a DFS tree. These graphs are called Total −DFS −Graphs. We prove that ...
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