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Carlitz L (1969) Kloosterman sums and finite field extensions. Acta Arith 16:179–193
Creignou N, Khanna S, Sudan M (2001) Complexity classifications of boolean constraint satisfaction problems. SIAM monographs on discrete mathematics and applications. Society for Industrial and Applied Mathematics, Philadelphia
Dyer M, Greenhill C (2000) The complexity of counting graph homomorphisms. Random Struct Algorithms 17(3–4):260–289
Freedman M, Lovász L, Schrijver A (2007) Reflection positivity, rank connectivity, and homomorphism of graphs. J Am Math Soc 20:37–51
Goldberg L, Grohe M, Jerrum M, Thurley M (2010) A complexity dichotomy for partition functions with mixed signs. SIAM J Comput 39(7):3336–3402
Grohe M, Thurley M (2011) Counting homomorphisms and partition functions. In: Grohe M, Makowsky J (eds) Model theoretic methods in finite combinatorics. Contemporary mathematics, vol 558. American Mathematical Society, Providence
Hell P, Nešetřil J (1990) On the complexity of H-coloring. J Comb Theory Ser B 48(1):92–110
Ladner R (1975) On the structure of polynomial time reducibility. J ACM 22(1):155–171
Lidl R, Niederreiter H (1997) Finite fields. Encyclopedia of mathematics and its applications, vol 20. Cambridge University Press, Cambridge
Linial N (1986) Hard enumeration problems in geometry and combinatorics. SIAM J Algebraic Discret Methods 7:331–335
Schaefer T (1978) The complexity of satisfiability problems. In: Proceedings of the 10th annual ACM symposium on theory of computing, San Diego, California, pp 216–226
Vadhan S (2002) The complexity of counting in sparse, regular, and planar graphs. SIAM J Comput 31:398–427
Valiant L (1979) The complexity of computing the permanent. Theor Comput Sci 8:189–201
Valiant L (1979) The complexity of enumeration and reliability problems. SIAM J Comput 8:410–421
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Cai, JY., Chen, X., Lu, P. (2016). Complexity Dichotomies for Counting Graph Homomorphisms. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_747
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