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The strong chromatic index of a graph G is the minimum integer k such that the edge set of G can be partitioned into k induced matchings. Faudree et al. (1990) 205–211] proposed an open problem: If G is bipartite and if for each edge x y ∈ E(G), d(x) + d(y) ≤ 5, then sχ (G) ≤ 6. Let H 0 be the graph obtained from a 5-cycle by adding a new vertex and joining… (More)

This paper studies circular chromatic numbers and fractional chromatic numbers of distance graphs G(Z , D) for various distance sets D. In particular, we determine these numbers for those D sets of size two, for some special D sets of size three, for D = {1,

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