A critical dilute O(n) model on the kagome lattice is investigated analytically and numerically. We employa number of exact equivalences which, in a few steps, link the critical O(n) spin model on the kagome latticetothe exactly solvable critical q-state Potts model on the honeycomb lattice with q= (n+1) 2. The intermediatesteps involve the random-cluster model on the honeycomb lattice and a fully packed loop model with loopweight n'=q and a dilute loop model with loop weight n, both on the kagome lattice. This mapping enablesthe determination ofa branch of critical points of the dilute O（n）model, as well as some of its criticalproperties. These properties differ from those of the generic O（n）critical points. For n=0, our model reproducesthe known universal properties of the point describing the collapse of a polymer. For n≠0 it displaysa line of multicritical points, with the same universal behavior as a branch of critical points that was foundearlier in a dilute O（n）model on the square lattice. These findings are supported by a finite-size-scalinganalysis in combination with transfer-matrix calculations.