Abstract

Publisher Summary This chapter discusses problems related to bipartite large chromatic graphs. It is assumed that the chromatic number χ(Ң) of a graph Ң is greater than κ, a finite or infinite cardinal. This problem is investigated in the chapter, in case some other restrictions are imposed on Ң as well. The results show that χ(Ң) can be arbitrarily large while the finite subgraphs are very close to bipartite graphs. This topic is a strange mixture of finite combinatorics and set theory. There is a striking difference between large chromatic finite and infinite graphs, which was discovered by the first two authors about fifteen years ago. While for any k κ without any short circuits, a graph with χ(Ң) > κ ≥ ω has to contain a complete bipartite graph [ k , κ + ] for all k

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