babak's blog

Girth of Graph
By babak, 12 years ago, In English

Let G be a graph with n vertices and Δ(G)≤10 . find an algorithm with O(n) compolexity to determine this graph has girth less than 20 or not ?

thanks for any hint :)

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12 years ago, # |
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what is less than or equal to 10? number of vertices? with n <= 10 we can just check all possible subsets.

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    12 years ago, # ^ |
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    I think Δ(G) means the maximum degree of vertices on G.

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12 years ago, # |
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The solution is as straightforward as it is practically useless. Let's use brute-force backtracking algorithm to find all paths of length no more than 20, and check if any of them is a cycle. It will do about n*10^20 operations, which is still O(n).

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