Sufficient Condition and Algorithm for Hamiltonian in 3-Connected 3-Regular Planar Bipartite Graph

Md. Khaliluzzaman, Md. Monirul Islam, Md. Monjur Hasan
2015 International Journal of Computer Applications  
A graph G (V, E) is said to be Hamiltonian if it contains a spanning cycle. The spanning cycle is called a Hamiltonian cycle of G and G is said to be a Hamiltonian graph. A Hamiltonian path is a path that contains all the vertices in V (G) but does not return to the vertex in which it began. In this paper, we study Hamiltonicity of 3-connected, 3-regular planar bipartite graph G with partite sets V=M  N. We shall prove that G has a Hamiltonian cycle if G is balanced with M = N. For that we
more » ... ent an algorithm for a bipartite graph K M,N where M>3, N>3 and M,N both are even to possess a Hamiltonian cycle. In particular, we also prove a theorem for S proper subset (M or N) of V the number of components W (G-S) = S implies the graph has a Hamiltonian path.
doi:10.5120/20596-3096 fatcat:tejwu5a2lva5toxq5s47sqxipi