An efficient algorithm to solve connectivity problem on trapezoid graphs

The connectivity problem is a fundamental problem in graph theory. The best known algorithm to solve the connectivity problem on general graphs withn vertices andm edges takesO(K(G)mn1.5) time, whereK(G) is the vertex connectivity ofG. In this paper, an efficient algorithm is designed to solve vertex connectivity problem, which takesO(n2) time andO(n) space for a trapezoid graph.