Square Hamiltonian cycles in graphs with maximal 4-cliques

AbstractThe square of a graph is obtained by adding additional edges joining all pairs of vertices with distance two in the original graph. Pósa conjectured that if G is a simple graph on n vertices with minimum degree 2n/3, then G contains the square of a hamiltonian cycle. We show that Pósa's conjecture holds for graphs that in addition contain a maximal 4-clique