Find the minimum number of nodes to be removed to convert a graph into a tree.
number of nodes < 1e5
number of edges < 2e5
Any help, please...
# | User | Rating |
---|---|---|
1 | tourist | 4009 |
2 | jiangly | 3773 |
3 | Radewoosh | 3646 |
4 | ecnerwala | 3624 |
5 | jqdai0815 | 3620 |
5 | Benq | 3620 |
7 | orzdevinwang | 3612 |
8 | Geothermal | 3569 |
8 | cnnfls_csy | 3569 |
10 | gyh20 | 3447 |
# | User | Contrib. |
---|---|---|
1 | awoo | 161 |
2 | maomao90 | 160 |
3 | nor | 157 |
4 | atcoder_official | 156 |
4 | cry | 156 |
6 | -is-this-fft- | 155 |
7 | maroonrk | 154 |
8 | adamant | 153 |
9 | Um_nik | 151 |
10 | djm03178 | 146 |
Find the minimum number of nodes to be removed to convert a graph into a tree.
number of nodes < 1e5
number of edges < 2e5
Any help, please...
Name |
---|
Auto comment: topic has been updated by b_like_karthik (previous revision, new revision, compare).
This problem is NP complete.
I quote from the paper "Maximum induced trees in graphs" by Paul Erdös, Michael Saks and Vera T Sós:
"The problem “given a graph H and integer k does H have an independent set of size k?” is a well-known NP-complete problem. Given H and k, let n be the number of vertices of H and let G be the graph obtained by adjoining a path on n vertices to H, one endpoint of which is joined by an edge to every vertex in H. The problem of whether H has an independent set of size k is easily seen to be equivalent to whether G has an induced tree of size n + k."
Source: https://doi.org/10.1016/0095-8956(86)90028-6
Therefore I doubt that an algorithm exists that can solve this problem for such large graphs in reasonable time.
Thank you very much