Speaker : Prof. Lih-hsing Hsu (Providence University) Title : Some construction methods for cubic 1p-fault tolerant Hamiltonian and 1-edge Hamiltonian laceable graphs and some construction methods for cubic 1-fault tolerant Hamiltonian graphs Time : 2017-12-05 (Tue) 15:00 - 16:00 Place : Seminar Room 617, Institute of Mathematics (NTU Campus) Abstract: A graph G = (V,E) is Hamiltonian if there exists a spanning cycle in G. A Hamiltonian graph G =(V,E) is 1-vertex fault tolerant Hamiltonian if G－F remains Hamiltonian for any fault F that is a vertex in V. A Hamiltonian graph G = (V,E) is 1-edge fault tolerant Hamiltonian if G－F remains Hamiltonian for any fault F that is an edge in E. A graph is 1-fault tolerant Hamiltonian if it is 1-vertex fault tolerant Hamiltonian and 1-edge fault tolerant Hamiltonian. A graph is Hamiltonian connected if there exists a Hamiltonian path between any two different vertices in G. A bipartite Hamiltonian graph G = ( B∪W , E) is 1p-fault tolerant Hamiltonian if G－F remains Hamiltonian for any fault F that is consisted of a vertex in B and a vertex in W. A bipartite graph G = ( B∪W , E) is Hamiltonian laceable if there exists a Hamiltonian path between any vertex in B and any vertex in W. A bipartite graph is 1-edge fault tolerant Hamiltonian laceable if G－F remains Hamiltonian laceable for any fault F that is an edge in E. In this talk, I will introduce some construction schemes for cubic bipartite graphs that are 1p-fault tolerant Hamiltonian and 1-edge Hamiltonian laceable and some construction schemes for cubic 1-fault tolerant Hamiltonian graphs.