Local and global proportionality
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Abstract The problem considered here is that posed by Fishburn, Hwang and Lee concerning the proportion of elements of one colour in a 2-coloured ring. It is required to deduce global information about this proportion from rather restricted local information. The problem is more or less solved for simple rings, some bounds are obtained in general, and conjectures are made concerning both the original problem and its generalizations to different sorts of graph.
[1] Peter C. Fishburn,et al. Do local majorities force a global majority? , 1986, Discret. Math..