The chromatic sum of a graph: history and recent developments
The chromatic sum of a graph is the smallest sum of colors among all proper colorings with natural numbers. The strength of a graph is the minimum number of colors necessary to obtain its chromatic sum. A natural generalization of chromatic sum is optimum cost chromatic partition (OCCP) problem, whe...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204306216 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | The chromatic sum of a graph is the
smallest sum of colors among all proper colorings with natural
numbers. The strength of a graph is the minimum number
of colors necessary to obtain its chromatic sum. A natural
generalization of chromatic sum is optimum cost chromatic
partition (OCCP) problem, where the costs of colors can be
arbitrary positive numbers. Existing results about chromatic sum,
strength of a graph, and OCCP problem are presented together with
some recent developments. The focus is on polynomial algorithms
for some families of graphs and NP-completeness issues. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |