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The time complexity to test whether a graph is bipartite or not is said to be _______ using depth first search.(a) O(n^3)(b) linear time(c) O(1)(d) O(nlogn)This question was posed to me in class test.The above asked question is from Bipartite Graphs topic in section Graphs of Discrete Mathematics

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Right choice is (b) linear time

The best explanation: It is possible to test whether a graph is bipartite, and to return EITHER a two-coloring (if it is bipartite) or an ODD cycle (if it is not) in linear time i.e, O(n) using depth first search. In case of the intersection of n line segments or other simple SHAPES in the EUCLIDEAN graph, it is possible to test whether the graph is bipartite and it will return either a two-coloring or an odd cycle in time O(nlogn), even though the graph itself has up to O(n^2) edges.


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