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...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204306216 |
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| _version_ | 1832556594268733440 |
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| author | Ewa Kubicka |
| author_facet | Ewa Kubicka |
| author_sort | Ewa Kubicka |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-122710aac9134cd2b62d5f818deadeaa |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-122710aac9134cd2b62d5f818deadeaa2025-02-03T05:44:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004301563157310.1155/S0161171204306216The chromatic sum of a graph: history and recent developmentsEwa Kubicka0Department of Mathematics, University of Louisville, Louisville 40292, KY, USAThe 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.http://dx.doi.org/10.1155/S0161171204306216 |
| spellingShingle | Ewa Kubicka The chromatic sum of a graph: history and recent developments International Journal of Mathematics and Mathematical Sciences |
| title | The chromatic sum of a graph: history and recent developments |
| title_full | The chromatic sum of a graph: history and recent developments |
| title_fullStr | The chromatic sum of a graph: history and recent developments |
| title_full_unstemmed | The chromatic sum of a graph: history and recent developments |
| title_short | The chromatic sum of a graph: history and recent developments |
| title_sort | chromatic sum of a graph history and recent developments |
| url | http://dx.doi.org/10.1155/S0161171204306216 |
| work_keys_str_mv | AT ewakubicka thechromaticsumofagraphhistoryandrecentdevelopments AT ewakubicka chromaticsumofagraphhistoryandrecentdevelopments |