Some Ramsey–Turán type problems and related questions

In this paper the following Ramsey–Turán type problem is one of several addressed. For which graphs GG does there exist a constant 0c|H|δ(H)>c|H|, then any 2-edge coloring of HH contains a monochromatic copy of GG? Specific results, conjectures, and questions with suggested values for cc are considered when GG is an odd cycle, path, or tree of limited maximum degree. Another variant is to 2-edge color a replacement for the graph Kr(G)Kr(G) by a balanced multipartite graph of approximately the same order with the same consequence, a monochromatic GG.