Research on graphs characterized by forbidden minors

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From a given graph G, a graph obtained from a subgraph of G by contracting several edges is called a minor of G. Some important classes of graphs, such as planar graphs are closed under the operation taking a minor, and are characterized by forbidden minors. In this research, we extend some results of planar graphs concerning cycles, spanning trees and factors, from the point of view of forbidden minors. In particular, we obtained some results on the toughness and the spanning trees in graphs without complete bipartite minors. We also considered similar problems on the forbidden induced subgraphs.