Fractional chromatic number of distance graphs generated by two-interval sets
- Liu, Daphne Der-Fen
- Zhu, Xuding
DOIAbstract
AbstractLet D be a set of positive integers. The distance graph generated by D, denoted by G(Z,D), has the set Z of all integers as the vertex set, and two vertices x and y are adjacent whenever |x−y|∈D. For integers 1<a≤b<m−1, define Da,b,m={1,2,…,a−1}∪{b+1,b+2,…,m−1}. For the special case a=b, the chromatic number for the family of distance graphs G(Z,Da,a,m) was first studied by R.B. Eggleton, P. Erdős and D.K. Skilton [Colouring the real line, J. Combin. Theory (B) 39 (1985) 86–100] and was completely solved by G. Chang, D. Liu and X. Zhu [Distance graphs and T-coloring, J. Combin. Theory (B) 75 (1999) 159–169]. For the general case a≤b, the fractional chromatic number for G(Z,Da,b,m) was studied by P. Lam and W. Lin [Coloring distance ...
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