Hamilton-connected properties of 3-connected {claw, hourglass, bull}-free graphs

An hourglass is the graph with degree sequence . In this paper, for integers , the bull is the graph obtained by attaching endvertices of two disjoint paths of lengths to two vertices of a triangle. We show that every 3-connected -free graph, where , is Hamilton-connected. Moreover, we give an example to show the sharpness of our result, and complete the characterization of forbidden induced bulls implying Hamilton-connectedness of a 3-connected {claw, hourglass, bull}-free graph.