Wild edge colourings of graphs

Journal of Symbolic Logic 69 (1):255 - 264 (2004)
We prove consistent, assuming there is a supercompact cardinal, that there is a singular strong limit cardinal $\mu$ , of cofinality $\omega$ , such that every $\mu^{+}$ -chromatic graph X on $\mu^{+}$ has an edge colouring c of X into $\mu$ colours for which every vertex colouring g of X into at most $\mu$ many colours has a g-colour class on which c takes every value. The paper also contains some generalisations of the above statement in which $\mu^{+}$ is replaced by other cardinals < $\mu$
Keywords Prikry forcing   chromatic number   graph colourings
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