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We present results referring to the Hadwiger-Nelson problem which asks for the minimum number of colours needed to colour the plane with no two points at distance 1 having the same colour. Exoo considered a more general problem concerning graphs G_[a,b] with R^2 as the vertex set and two vertices adjacent if their distance is in the interval [a,b]. Exoo conjectured χ(G_[a,b]) = 7 for sufficiently small but positive difference between a and b. We partially answer this conjecture by proving thatdoi:10.1007/s00454-016-9769-3 fatcat:aetxp63a2raaffvf77oywtiodm