On a theorem about vertex colorings of graphs
A nice and short proof is given of the following Theorem: ``Let G be a finite graph. Let \(f_ 0,f_ 1,...,f_ n\) be real-valued functions on V(G) such that for every vertex v, \(\sum_{i}f_ i(v)>d(v)\) (the degree of v). Then there exists a colouring c: V(G)\(\to \{0,1,...,n\}\) such that every vertex v is adjacent to fewer than \(f_{c(v)}(v)\) vertices with the same colour as v'', which is due to \textit{J. Lawrence} [Discr. Math. 21, 61-68 (1978; Zbl 0371.05024)] and \textit{O. V. Borodin} and \textit{A. V. Kostochka} [J. Comb. Theory, Ser. B 23, 247-250 (1977; Zbl 0336.05104)].
scientific article; zbMATH DE number 4014749