Citation
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
Abstract
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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