Hamilton-connected {claw, bull}-free graphs

The generalized bull is the graph Bi,j ${B}_{i,j}$ obtained by attaching endvertices of two disjoint paths of lengths i,j $i,j$ to two vertices of a triangle. We prove that every 3-connected {K1,3,X} $\{{K}_{1,3},X\}$-free graph, where X is an element of{B1,6,B2,5,B3,4} $X\in \{{B}_{1,6},{B}_{2,5},{B}_{3,4}\}$, is Hamilton-connected. The results are sharp and complete the characterization of forbidden induced bulls implying Hamilton-connectedness of a 3-connected {claw, bull}-free graph.