An Counterexample to the Proposition about Special Generating Subgraph of Hamiltonian Graph

Abstract:

      Theorem 3 in [l] states that any Hamiltonian graph must contain an alternate even-cycle connecting p subcycles with p bridges (p ≥ 2), here the p subcycles are elementary and disconnected one another. In this paper we give a counterexample to this proposition. In addition, we substitute some conclusions for it.