The Duchet conjecture
In this paper, we investigate a conjecture of Duchet that r(G)≤η(G)+1, where r(G) is the Radon number and η(G) is the Hadwiger number of a graph G. In this paper, we give a class of counter examples for which rg(G)=η(G)+2, where rg(G) is the Radon number for the g-convexity structure. On the positiv...
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Indian National Science Academy
1998
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| Online Access: | http://psasir.upm.edu.my/id/eprint/51724/1/51724.pdf http://psasir.upm.edu.my/id/eprint/51724/ |
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my.upm.eprints.517242017-09-05T09:07:21Z http://psasir.upm.edu.my/id/eprint/51724/ The Duchet conjecture Prakash, V. Parthasarathy, K. R. Rangan, C. Pandu In this paper, we investigate a conjecture of Duchet that r(G)≤η(G)+1, where r(G) is the Radon number and η(G) is the Hadwiger number of a graph G. In this paper, we give a class of counter examples for which rg(G)=η(G)+2, where rg(G) is the Radon number for the g-convexity structure. On the positive side, we prove the conjecture for some special classes of graphs like cycles and chordal graphs. Indian National Science Academy 1998 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/51724/1/51724.pdf Prakash, V. and Parthasarathy, K. R. and Rangan, C. Pandu (1998) The Duchet conjecture. Indian Journal of Pure and Applied Mathematics, 29 (4). pp. 447-459. ISSN 0019-5588; ESSN: 0975-7465 |
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English |
| description |
In this paper, we investigate a conjecture of Duchet that r(G)≤η(G)+1, where r(G) is the Radon number and η(G) is the Hadwiger number of a graph G. In this paper, we give a class of counter examples for which rg(G)=η(G)+2, where rg(G) is the Radon number for the g-convexity structure. On the positive side, we prove the conjecture for some special classes of graphs like cycles and chordal graphs. |
| format |
Article |
| author |
Prakash, V. Parthasarathy, K. R. Rangan, C. Pandu |
| spellingShingle |
Prakash, V. Parthasarathy, K. R. Rangan, C. Pandu The Duchet conjecture |
| author_facet |
Prakash, V. Parthasarathy, K. R. Rangan, C. Pandu |
| author_sort |
Prakash, V. |
| title |
The Duchet conjecture |
| title_short |
The Duchet conjecture |
| title_full |
The Duchet conjecture |
| title_fullStr |
The Duchet conjecture |
| title_full_unstemmed |
The Duchet conjecture |
| title_sort |
duchet conjecture |
| publisher |
Indian National Science Academy |
| publishDate |
1998 |
| url |
http://psasir.upm.edu.my/id/eprint/51724/1/51724.pdf http://psasir.upm.edu.my/id/eprint/51724/ |
| _version_ |
1643835036746645504 |
| score |
13.211869 |