An exact value for the path-chromatic index of a complete graph
We prove that the edge of <em>K</em><sub><em>n</em></sub> cannot be partitioned into less than <em>(n-1)/t P</em><sub><em>i+2</em></sub>-free subgraphs. We show that this inequality is sharp and characterize the edge partition...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Università degli Studi di Catania
1989-10-01
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| Series: | Le Matematiche |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/691 |
| _version_ | 1828916789563621376 |
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| author | Frank Harary Źsolt Tuza |
| author_facet | Frank Harary Źsolt Tuza |
| author_sort | Frank Harary |
| collection | DOAJ |
| description | We prove that the edge of <em>K</em><sub><em>n</em></sub> cannot be partitioned into less than <em>(n-1)/t P</em><sub><em>i+2</em></sub>-free subgraphs. We show that this inequality is sharp and characterize the edge partitions which attain it. In the process, we point out a surprising connection between the combinatorial designs and the conditional chromatic index. |
| first_indexed | 2024-12-13T20:39:07Z |
| format | Article |
| id | doaj.art-5bcb5f7bab48421aa9b6dad47db07fe3 |
| institution | Directory Open Access Journal |
| issn | 0373-3505 2037-5298 |
| language | English |
| last_indexed | 2024-12-13T20:39:07Z |
| publishDate | 1989-10-01 |
| publisher | Università degli Studi di Catania |
| record_format | Article |
| series | Le Matematiche |
| spelling | doaj.art-5bcb5f7bab48421aa9b6dad47db07fe32022-12-21T23:32:12ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52981989-10-01442345350657An exact value for the path-chromatic index of a complete graphFrank HararyŹsolt TuzaWe prove that the edge of <em>K</em><sub><em>n</em></sub> cannot be partitioned into less than <em>(n-1)/t P</em><sub><em>i+2</em></sub>-free subgraphs. We show that this inequality is sharp and characterize the edge partitions which attain it. In the process, we point out a surprising connection between the combinatorial designs and the conditional chromatic index.http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/691 |
| spellingShingle | Frank Harary Źsolt Tuza An exact value for the path-chromatic index of a complete graph Le Matematiche |
| title | An exact value for the path-chromatic index of a complete graph |
| title_full | An exact value for the path-chromatic index of a complete graph |
| title_fullStr | An exact value for the path-chromatic index of a complete graph |
| title_full_unstemmed | An exact value for the path-chromatic index of a complete graph |
| title_short | An exact value for the path-chromatic index of a complete graph |
| title_sort | exact value for the path chromatic index of a complete graph |
| url | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/691 |
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