Motivated by work of Erdős, Ota determined the maximum size g(n,k) a k-connected nonhamiltonian graph order n in 1995. But for some pairs n,k, is not attained connectivity k. For example, g(15,3)=77 unique 7, 3. In this paper we obtain more precise information determining and k, extremal graphs. Consequently solve corresponding problem nontraceable

Let C be a class of graphs. A definition of a C-homogeneous graph G is given that generalizes that of C-ultrahomogeneous graph by considering each induced subgraph of G in C tethered by an arc. Let 2 < r ∈ Z, σ ∈ (0, r − 1) ∩ Z, t = 2 − 1 and s = 2. We require G to have each edge shared by exactly one copy of the complete subgraph K2s and one of the Turán graph Tts,t. Letting C = {K2s, Tts,t} l...