Forbidden subgraphs and the existence of cycles passing through specified vertices
My research theme is graph theory. Especially, the existence of partial structures of graphs such as the cycle and passing is researched. The cycle that passing through all the vertices in the graph is called a Hamilton cycle. The Hamilton problem has long been fundamental in graph theory.On the other hand what character have by the graph where a specific partial structure was prohibited on the other hand is researched. To prohibit the incduced subgraph is to specify the structure of the local in the graph. As a result, it can know information on the entire graph. Such a research is a very important research because it knows the structure of the graph. Moreover, the result can expect the application to various fields. In this research, hamiltonicity in graph where specific partial structure was prohibited was researched. The problem in the future is that the structure of a graph where connected level is high is specified.