For every finite m and n there is a finite set {G 1 , . . . , G l } of countable (m • K n )-free graphs such that every countable (m • K n )-free graph occurs as an induced subgraph of one of the graphs G i .
Sum Multicoloring of Graphs
✍ Scribed by Amotz Bar-Noy; Magnús M. Halldórsson; Guy Kortsarz; Ravit Salman; Hadas Shachnai
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 176 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0196-6774
No coin nor oath required. For personal study only.
✦ Synopsis
Scheduling dependent jobs on multiple machines is modeled by the graph multicoloring problem. In this paper we consider the problem of minimizing the average completion time of all jobs. This is formalized as the sum multicoloring problem: Given a graph and the number of colors required by each vertex, find a multicoloring which minimizes the sum of the largest colors assigned to the 1
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