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In this paper we have proved that every 3-connected K_{1;3}B_{2;5} (or K_{1;3}B_{3;4})-free graph is Hamiltonian.EVERY 3-CONNECTED CLAW-FREE Bi;7i-FREE GRAPH IS HAMILTONIAN KHIKMAT SABUROV1;, MANSOOR SABUROV2 1Department of Mathematics, University of West Bohemia, and Institute for Theoretical Computer Science (ITI), Charles University, P.O