First-Fit Coloring of Forests in Random Arrival Model
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913461111357440 |
|---|---|
| author | Bosek, Bartłomiej Gutowski, Grzegorz Lasoń, Michał Przybyło, Jakub |
| author_facet | Bosek, Bartłomiej Gutowski, Grzegorz Lasoń, Michał Przybyło, Jakub |
| contents | We consider a graph coloring algorithm that processes vertices in order taken uniformly at random and assigns colors to them using First-Fit strategy. We show that this algorithm uses, in expectation, at most $(1 + o(1))\cdot \ln n \,/\, \ln\ln n$ different colors to color any forest with $n$ vertices. We also construct a family of forests that shows that this bound is best possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17011 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | First-Fit Coloring of Forests in Random Arrival Model Bosek, Bartłomiej Gutowski, Grzegorz Lasoń, Michał Przybyło, Jakub Discrete Mathematics We consider a graph coloring algorithm that processes vertices in order taken uniformly at random and assigns colors to them using First-Fit strategy. We show that this algorithm uses, in expectation, at most $(1 + o(1))\cdot \ln n \,/\, \ln\ln n$ different colors to color any forest with $n$ vertices. We also construct a family of forests that shows that this bound is best possible. |
| title | First-Fit Coloring of Forests in Random Arrival Model |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2404.17011 |