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Title: Graph Family Operations

Abstract: (based on a paper by Paul Catlin, Arthur Hobbs, and Hong-Jian Lai)
Paralleling the study of forbidden minors, we examine sets of graphs satisfying conditions of forbidden subgraphs, forbidden contractions, and forbidden CH-morphs (which will be defined in the talk). For these classes of graphs, we cannot get anything like the wonderful results of Robertson and Seymour found for forbidden graph minors. But we do get some very interesting relationships and results for our classes, and we show that there are many important classes of graphs that fit these descriptions.

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