Forbidden subgraphs for graphs with (near) perfect matching to be Hamiltonian

Let G = (V (G), E(G)) be a graph. A set M ⊆ E(G) is a matching if no two edges in M share a common vertex. A matching of G is perfect if it covers every vertex in G. A matching of a graph G with odd order is called a near perfect matching if it has (Figure presented.) edges. In this paper, we completely characterize the forbidden subgraph and pairs of forbidden subgraphs that force a 2-connected graph with a (near) perfect matching to be hamiltonian.