Wild edge colourings of graphs

Journal of Symbolic Logic 69 (1):255-264 (2004)
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Abstract

We prove consistent, assuming there is a supercompact cardinal, that there is a singular strong limit cardinalμ, of cofinalityω, such that everyμ+-chromatic graphXonμ+has an edge colouringcofXintoμcolours for which every vertex colouringgofXinto at mostμmany colours has ag-colour class on whichctakes every value.The paper also contains some generalisations of the above statement in whichμ+is replaced by other cardinals >μ.

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