Diastereoselective Lithiation-Substitution of N-Silyl-Protected-(S)-Tetrahydro-1H-pyrrolo[1,2-c]imidazole-3(2H)-ones and Applications of Their Derivatives

This thesis describes a method involving the preparation of an L-proline-derived imidazolone protected with an N-triethylsilyl group that undergoes diastereoselective lithiation followed by electrophile quench to give C5-substituted products with syn stereochemistry. The N-silylated derivatives may be more easily N-deprotected as compared to previous N-t-Bu analogues to give secondary ureas. These may serve as precursors to N-phenyl chiral bicyclic guanidines or as NHC precursors for synthesis of corresponding complexes.

Diastereoselective Lithiation-Substitution of N-Silyl-Protected-(S)-Tetrahydro-1H-pyrrolo[1,2-c]imidazole-3(2H)-ones and Applications of Their Derivatives

This thesis describes a method involving the preparation of an L-proline-derived imidazolone protected with an N-triethylsilyl group that undergoes diastereoselective lithiation followed by electrophile quench to give C5-substituted products with syn stereochemistry. The N-silylated derivatives may be more easily N-deprotected as compared to previous N-t-Bu analogues to give secondary ureas. These may serve as precursors to N-phenyl chiral bicyclic guanidines or as NHC precursors for synthesis of corresponding complexes.

Backbone Colouring of Graphs

Consider an undirected graph G and a subgraph of G, H. A q-backbone k-colouring of (G,H) is a mapping f: V(G) {1, 2, ..., k} such that G is properly coloured and for each edge of H, the colours of its endpoints differ by at least q. The minimum number k for which there is a backbone k-colouring of (G,H) is the backbone chromatic number, BBCq(G,H). It has been proved that backbone k-colouring of (G,T) is at most 4 if G is a connected C4-free planar graph or non-bipartite C5-free planar graph or Cj-free, j∈{6,7,8} planar graph without adjacent triangles. In this thesis we improve the results mentioned above and prove that 2-backbone k-colouring of any connected planar graphs without adjacent triangles is at most 4 by using a discharging method. In the second part of this thesis we further improve these results by proving that for any graph G with χ(G) ≥ 4, BBC(G,T) = χ(G). In fact, we prove the stronger result that a backbone tree T in G exists, such that ∀ uv ∈ T, |f(u)-f(v)|=2 or |f(u)-f(v)| ≥ k-2, k = χ(G). For the case that G is a planar graph, according to Four Colour Theorem, χ(G) = 4; so, BBC(G,T) = 4.