The performance of the greedy coloring algorithm ''first fit'' on sparse random graphs G and on random trees is investigated. In each case, approximately n, c r n log log n colors are used, the exact number being concentrated almost surely on at 2 most two consecutive integers for a sparse random gr
Random coloring evolution on graphs
β Scribed by Xin Xing Chen; Jian Gang Ying
- Publisher
- Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
- Year
- 2010
- Tongue
- English
- Weight
- 178 KB
- Volume
- 26
- Category
- Article
- ISSN
- 1439-7617
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The graph coloring problem is to color a given graph with the minimum number of colors. This problem is known to be NP-hard even if we are only aiming at approximate solutions. On the other hand, the best known approximation algorithms require β¦ Ε½ . Ε½ . n β¦ ) 0 colors even for bounded chromatic k-co
## Abstract We prove that a 2βconnected, outerplanar bipartite graph (respectively, outerplanar nearβtriangulation) with a list of colors __L__ (__v__ ) for each vertex __v__ such that $|L(v)|\geq\min\{{\deg}(v),4\}$ (resp., $|L(v)|\geq{\min}\{{\deg}(v),5\}$) can be __L__βlistβcolored (except when