The Duchet conjecture

In this paper, we investigate a conjecture of Duchet that r(G)�?(G)+1, where r(G) is the Radon number and ?(G) is the Hadwiger number of a graph G. In this paper, we give a class of counter examples for which rg(G)=?(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.