• Beigel R, Eppstein D (2005) 3-coloring in time\(O(1.3289^n)\). J Algorithms 54:168–204

  Article MathSciNet MATH  Google Scholar 

• Bollobas B (1998) Modern graph theory. Springer, New York

  Book MATH  Google Scholar 

• Bjorklund A, Husfeldt T, Koivisto M (2009) Set partitioning via inclusion–exclusion. SIAM J Comput 39:546–563

  Article MathSciNet  Google Scholar 

• Byskov JM (2004) Enumerating maximal independent sets with applications to graph colouring. Oper Res Lett 32:547–556

  Article MathSciNet MATH  Google Scholar 

• Caramia M, Dell’Olmo P (2001) A lower bound on the chromatic number of Mycielski graphs. Discret Math 235:79–86

  Article MathSciNet MATH  Google Scholar 

• Chen BL, Huang KC, Yen HC (2008) Chromatic coloring with a maximum color class. Discret Math 308:5533–5537

  Article MathSciNet MATH  Google Scholar 

• Coja-Oghlan A, Panagiotou K, Steger A (2008) On the chromatic number of random graphs. J Combin Theory 98:980–993

  Article MathSciNet MATH  Google Scholar 

• De Werra D (1990) Heuristics for graph coloring. Computing 7:191–208

  Google Scholar 

• Di Nola A, Pedrycz W, Sessa S (1985a) Minimal and maximal solutions of a decomposition problem of fuzzy relations. Int J Gen Syst 11:103–112

  Article  Google Scholar 

• Di Nola A, Pedrycz W, Sessa S (1985b) Decomposition problem of fuzzy relation. Int J Gen Syst 10:123–133

  Article MATH  Google Scholar 

• Di Nola A, Pedrycz W, Sessa S (1985c) When is a fuzzy relation decomposable into fuzzy sets. Fuzzy Sets Syst 16:87–90

  Article MATH  Google Scholar 

• Fleurent C, Ferland JA (1996) Genetic and hybrid algorithms for graph coloring. Ann Oper Res 63:437–461

  Article MATH  Google Scholar 

• Galinier P, Hao JK (1999) Hybrid evolutionary algorithms for graph coloring. J Combin Optim 4:379–397

  Article MathSciNet  Google Scholar 

• Hell P, Pan ZS, Wong TL, Zhu XD (2009) Adaptable chromatic number of graph products. Discret Math 309:153–6159

  MathSciNet  Google Scholar 

• Herrmann F, Hertz A (2002) Finding the chromatic number by means of critical graphs. ACM J Exp Algorithm 7:1–9

  Article MathSciNet  Google Scholar 

• Jackowski B (1985) A generalized implicit enumeration algorithm for graph coloring. Commun ACM 28:412–418

  Article  Google Scholar 

• Liu XC (1996) The least upper bound of content for realizable matrices on lattice [0,1]. Fuzzy Sets Syst 80:257–259

  Article MATH  Google Scholar 

• Liu WJ (1982) The realizable problem for symmetric matrix. J Fuzzy Math 1:69–76 (in Chinese)

  Google Scholar 

• Mo Y, Wang XP (2011) An improved algorithm on the content of realizable fuzzy matrices. Soft Comput 15:1835–1843

  Article MATH  Google Scholar 

• Nobuhara H, Takama Y, Hirota K (2001) Fast iterative solving method of various types of fuzzy relational equations and its application to image reconstruction. Int J Adv Comput Intell 5:90–98

  Google Scholar 

• Nobuhara H, Pedrycz W, Hirota K (2002) A digital watermarking algorithm using image compression method based on fuzzy relational equation. Proceedings of the 2002 IEEE International Conference on Fuzzy Systems 2: 1568–1573

• Nobuhara H, Hirota K, Pedrycz W, Sessa S (2004) Two iterative methods of decomposition of a fuzzy relation for image compression/decompression processing. Soft Comput 8:698–704

  Article MATH  Google Scholar 

• Pedrycz W (1996) Classification of relational patterns as a decomposition problem. Pattern Recognit Lett 17:91–99

  Article  Google Scholar 

• Pedrycz W (1998) Optimization schemes for decomposition of fuzzy relations. Fuzzy Sets Syst 100:301–325

  Article MathSciNet MATH  Google Scholar 

• Pedrycz W, Hirota K, Sessa S (2001) A decomposition of fuzzy relations. IEEE Trans Syst Man Cybern B 31:657–663

  Article  Google Scholar 

• Vrba J (1993) General decomposition problem of fuzzy relation. Fuzzy Sets Syst 54:69–79

  Article MathSciNet MATH  Google Scholar 

• Wang MX (1984) The realizable conditions for fuzzy matrix and its content (in Chinese). J Fuzzy Math 1:51–58

  Google Scholar 

• Wang GP (1985) Some estimations of the least upper bound of content for realizable matrices on completely distributive lattice. J Fuzzy Math 2:65–74 (in Chinese)

  Google Scholar 

• Wang XP (2000) How to calculate the content for a given realzable fuzzy matrix. Indian J Pure Appl Math 31:327–339

  MathSciNet MATH  Google Scholar 

• Wang XP, Yang Y (2007) On the computational complexity of the schein rank of fuzzy relations. Math Numer Sin 29:273–284 (in Chinese)

  MathSciNet MATH  Google Scholar 

• Yang Y, Wang XP (2005) On the convergence exponent of decomposable fuzzy relations. Fuzzy Sets Syst 151:403–419

  Article MATH  Google Scholar 

• Yang Y, Wang XP (2007) The general a-decomposition problem of fuzzy relations. Inf Sci 177:4922–4933

  Article MATH  Google Scholar 

• Yu YD (1984) On the realizable L-fuzzy symmentric matrices. J Fuzzy Math 1:15–20 (in Chinese)

  Google Scholar 

• Zhao D (1985) The realizability of fuzzy symmetric matrices. J Fuzzy Math 1:1–8 (in Chinese)

  Google Scholar 

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