Long cycles in triangle-free graphs with prescribed independence number and connectivity

The Chvátal-Erdős theorem says that a 2-connected graph with α(G)⩽κ(G) is hamiltonian. We extend this theorem for triangle-free graphs. We prove that if G is a 2-connected triangle-free graph of order n with α(G)⩽2κ(G)−2, then every longest cycle in G is dominating, and G has a cycle of length at least min{n−α(G)+κ(G),n}.