| # | User | Rating |
|---|---|---|
| 1 | tourist | 4009 |
| 2 | jiangly | 3831 |
| 3 | Radewoosh | 3646 |
| 4 | jqdai0815 | 3620 |
| 4 | Benq | 3620 |
| 6 | orzdevinwang | 3529 |
| 7 | ecnerwala | 3446 |
| 8 | Um_nik | 3396 |
| 9 | gamegame | 3386 |
| 10 | ksun48 | 3373 |
| # | User | Contrib. |
|---|---|---|
| 1 | cry | 164 |
| 1 | maomao90 | 164 |
| 3 | Um_nik | 163 |
| 4 | atcoder_official | 160 |
| 5 | -is-this-fft- | 158 |
| 6 | awoo | 157 |
| 7 | adamant | 156 |
| 8 | TheScrasse | 154 |
| 8 | nor | 154 |
| 10 | Dominater069 | 153 |
Let G be a graph so that for every v, deg(v) ≥ k. Show that G contains a path of length at least k and give an algorithm to find such a path.
Hint: Augment a path from both ends until there are no vertices outside the path, that are joined to the end vertices of the path.
Choose any vertex v in the first step. At each subsequent step, choose any random neighbor of the current vertex you are in that has not been visited before. You will get a valid choice for the next vertex for all the first k steps because each vertex has at least k neighbors and less than k vertices have been marked as visited.