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This paper gives non-embeddings and non-immersions for the real flag manifolds R F ( 1 , l,n -2),n > 3 and shows that Lam's immersions for n = 4 and 5 and Stong's result for n = 6 are the best possible.

Let L2n stand for the sunlet graph which is a graph that consists of a cycle and an edge terminating in a vertex of degree one attached to each vertex of cycle Cn. The necessary condition for the equipartite graph Kn+I*K̅m to be decomposed into L2n for n≥2 is that the order of L2n must divide n2m2/2, the order of Kn+I*K̅m. In this work, we show that this condition is sufficient for the decomposition. The proofs are constructive using graph theory techniques.

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