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And Szemeredi, E. (1995) Dense graphs without 3-regular subgraphs. J. Combin. Theory Ser. B 63 41-54. -W. (1976) Uber eine Vermutung in der additiven Zahlentheorie, PhD thesis, Tech. Univ. Braunschweig. [51] Rodseth, 6 . J. (1994) Sums of distinct residues mod p. Acta Arith. 65 181-184. [52] Scheim, D. E. (1974) The number of edge 3-colorings of a planar cubic graph as a permanent. Discrete Math. 8 377-382. [53] Schmidt, W. (1976) Equations over Finite Fields: An Elementary Approach, Vol. 536 of Lecture Notes in Mathematics, Springer, Berlin.

Several extensions are proved in [7]. 18 N. Alon 7. Graph colouring Graph colouring is arguably the most popular subject in graph theory. An interesting variant of the classical problem of colouring properly the vertices of a graph with the minimum possible number of colours arises when one imposes some restrictions on the colours available for every vertex. This variant received a considerable amount of attention that led to several fascinating conjectures and results, and its study combines interesting combinatorial techniques with powerful algebraic and probabilistic ideas.

58] Vizing, V. G. (1964) On an estimate on the chromatic class of a p-graph. Diskret. Analiz. 3 25-30. In Russian. [59] Vizing, V G. (1976) Coloring the vertices of a graph in prescribed colors (in Russian), Diskret. Analiz. No. 29, Metody Diskret. Anal. v. Teorii Kodov i Shem 101 3-10. [60] van der Waerden, B. L. (1931) Modern Algebra, Julius Springer, Berlin. [61] Yuzvinsky, S. (1981) Orthogonal pairings of Euclidean spaces. Michigan Math. J. 28 109-119. Combinatorics, Probability and Computing (1999) 8, 31—43.

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