For integers p, q, s with p ≥ q ≥ 2 and s ≥ 0, let K−s 2 (p, q) denote the set of 2−connected bipartite graphs which can be obtained from Kp,q by deleting a set of s edges. F.M.Dong et al. (Discrete Math. vol.224 (2000) 107–124) proved that for any graph G ∈ K−s 2 (p, q) with p ≥ q ≥ 3 and 0 ≤ s ≤ min{4, q−1}, then G is chromatically unique. In this paper, we shall extend this result to p ≥ q ≥...

We present five-loop results for the renormalization of various models with a cubic interaction (in ${d = 6 - 2 \varepsilon}$ dimensions). For scalar model and its ${O(n)}$-symmetric extension we provide constants, anomalous dimensions critical exponents. discuss in detail method calculation, all counterterms up to five loops. This allows one consider generalizations ${\varphi^3}$ theory other ...