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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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