Erratum to: "Fractional chromatic number and circular chromatic number for distance graphs with large clique size" Journal of Graph Theory 47(2) 2004, 129-146
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Let m ≥ 0 be the smallest integer such that S ∩ Ti−a+(m−1)(b−a) = Ø or i+b+m(b−a) ≥ a+c. If S∩Ti−a+(m−1)(b−a) = Ø, let i2 = i−a+(m−1)(b−a). Otherwise, let i2 = i+b+m(b−a). If it is the former case, then m ≥ 1 and i2 ∈ I (since i + b + (m− 1)(b− a) < a + c, so i2 = i− a + (m− 1)(b− a) < c− b = a). We now show that if it is the latter case, then i2 ∈ U . Assume i2 = i + b + m(b− a). Then i + b + (m− 1)(b− a) < a + c ≤ i + b + m(b− a), which implies
[1] Xuding Zhu,et al. Fractional chromatic number and circular chromatic number for distance graphs with large clique size , 2004, J. Graph Theory.