메뉴 건너뛰기




Volumn 343, Issue 1-4, 2004, Pages 401-423

On the phase transitions of graph coloring and independent sets

Author keywords

Acyclic orientations; Graph coloring; Maximum independent sets; Phase transitions

Indexed keywords

CORRELATION METHODS; GRAPH THEORY; NUMBER THEORY; OPTIMIZATION; POLYNOMIALS; PROBABILITY; PROBLEM SOLVING; SET THEORY;

EID: 4544330463     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2004.05.055     Document Type: Article
Times cited : (10)

References (48)
  • 2
    • 0003037529 scopus 로고
    • Reducibility among combinatorial problems
    • R.E. Miller, J.W. Thatcher (Eds.), Plenum Press, New York, NY
    • R.M. Karp, Reducibility among combinatorial problems, in: R.E. Miller, J.W. Thatcher (Eds.), Complexity of Computer Computations, Plenum Press, New York, NY, 1972, pp. 85-103.
    • (1972) Complexity of Computer Computations , pp. 85-103
    • Karp, R.M.1
  • 4
    • 0001951331 scopus 로고
    • A catalog of complexity classes
    • J. van Leeuwen (Ed.), MIT Press, Cambridge, MA
    • D.S. Johnson, A catalog of complexity classes, in: J. van Leeuwen (Ed.), Handbook of Theoretical Computer Science, Vol. A, MIT Press, Cambridge, MA, 1990, pp. 67-161.
    • (1990) Handbook of Theoretical Computer Science , vol.A , pp. 67-161
    • Johnson, D.S.1
  • 7
    • 0033536221 scopus 로고    scopus 로고
    • Determining computational complexity from characteristic 'phase transitions'
    • R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, L. Troyansky, Determining computational complexity from characteristic 'phase transitions', Nature 400 (1999) 133-137.
    • (1999) Nature , vol.400 , pp. 133-137
    • Monasson, R.1    Zecchina, R.2    Kirkpatrick, S.3    Selman, B.4    Troyansky, L.5
  • 8
    • 0034320732 scopus 로고    scopus 로고
    • Phase transitions in relational learning
    • A. Giordana, L. Saitta, Phase transitions in relational learning, Mach. Learn. 41 (2000) 217-251.
    • (2000) Mach. Learn. , vol.41 , pp. 217-251
    • Giordana, A.1    Saitta, L.2
  • 9
    • 0034889013 scopus 로고    scopus 로고
    • Frozen development in graph coloring
    • J. Culberson, I. Gent, Frozen development in graph coloring, Theoret. Comput. Sci. 265 (2001) 227-264.
    • (2001) Theoret. Comput. Sci. , vol.265 , pp. 227-264
    • Culberson, J.1    Gent, I.2
  • 12
    • 0034886698 scopus 로고    scopus 로고
    • Statistical mechanics perspective on the phase transition in vertex covering of finite-connectivity random graphs
    • A.K. Hartmann, M. Weigt, Statistical mechanics perspective on the phase transition in vertex covering of finite-connectivity random graphs, Theoret. Comput. Sci. 265 (2001) 199-225.
    • (2001) Theoret. Comput. Sci. , vol.265 , pp. 199-225
    • Hartmann, A.K.1    Weigt, M.2
  • 13
    • 4544351391 scopus 로고    scopus 로고
    • Introduction to the second DIMACS challenge: Cliques, coloring, and satisfiability
    • D.S. Johnson, M.A. Trick, Providence, RI
    • D.S. Johnson, M.A. Trick, Introduction to the second DIMACS challenge: cliques, coloring, and satisfiability, in: D.S. Johnson, M.A. Trick, Cliques, Coloring, and Satisfiability, American Mathematical Society, Providence, RI, 1996, pp. 1-7.
    • (1996) Cliques, Coloring, and Satisfiability, American Mathematical Society , pp. 1-7
    • Johnson, D.S.1    Trick, M.A.2
  • 14
    • 0042492825 scopus 로고
    • The potts model
    • F.Y. Wu, The Potts model, Rev. Mod. Phys. 54 (1982) 235-268.
    • (1982) Rev. Mod. Phys. , vol.54 , pp. 235-268
    • Wu, F.Y.1
  • 15
    • 0035334408 scopus 로고    scopus 로고
    • Minimal vertex covers on finite-connectivity random graphs: A hard-sphere lattice-gas picture
    • M. Weigt, A.K. Hartmann, Minimal vertex covers on finite-connectivity random graphs: a hard-sphere lattice-gas picture, Phys. Rev. E 63 (2001) 056127.
    • (2001) Phys. Rev. E , vol.63 , pp. 056127
    • Weigt, M.1    Hartmann, A.K.2
  • 18
    • 4544284429 scopus 로고    scopus 로고
    • M.A. Trick, http://mat.gsia.cmu.edU/COLOR/solvers/trick.c.
    • Trick, M.A.1
  • 19
    • 0018456690 scopus 로고
    • New methods to color vertices of a graph
    • D. Brélaz, New methods to color vertices of a graph, Commun. ACM 22 (1979) 251-256.
    • (1979) Commun. ACM , vol.22 , pp. 251-256
    • Brélaz, D.1
  • 22
    • 0000192604 scopus 로고
    • Acyclic orientations of graphs
    • R.P. Stanley, Acyclic orientations of graphs, Discrete Math. 5 (1973) 171-178.
    • (1973) Discrete Math. , vol.5 , pp. 171-178
    • Stanley, R.P.1
  • 23
    • 0003652674 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, UK
    • R.P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge University Press, Cambridge, UK, 1999.
    • (1999) Enumerative Combinatorics , vol.2
    • Stanley, R.P.1
  • 24
    • 0035595038 scopus 로고    scopus 로고
    • Orientations acycliques et le polynôme chromatique
    • B. Lass, Orientations acycliques et le polynôme chromatique, Europ. J. Combin. 22 (2001) 1101-1123.
    • (2001) Europ. J. Combin. , vol.22 , pp. 1101-1123
    • Lass, B.1
  • 25
    • 0011652285 scopus 로고
    • Graph colorings and acyclic orientations
    • K.-P. Vo, Graph colorings and acyclic orientations, Linear Multilinear Algebra 22 (1987) 161-170.
    • (1987) Linear Multilinear Algebra , vol.22 , pp. 161-170
    • Vo, K.-P.1
  • 26
    • 0003652674 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, UK
    • R.P. Stanley, Enumerative Combinatorics, Vol. 1, Cambridge University Press, Cambridge, UK, 1997.
    • (1997) Enumerative Combinatorics , vol.1
    • Stanley, R.P.1
  • 27
    • 3543065651 scopus 로고
    • Acyclic orientations of a graph and chromatic and independence numbers
    • R.W. Deming, Acyclic orientations of a graph and chromatic and independence numbers, J. Combin. Theory Ser. B 26 (1979) 101-110.
    • (1979) J. Combin. Theory Ser. B , vol.26 , pp. 101-110
    • Deming, R.W.1
  • 28
    • 0000700209 scopus 로고
    • Nombre chromatique et plus longs chemins d'un graphe
    • B. Roy, Nombre chromatique et plus longs chemins d'un graphe, Revue AFIRO 1 (1967) 127-132.
    • (1967) Revue AFIRO , vol.1 , pp. 127-132
    • Roy, B.1
  • 29
    • 0004513558 scopus 로고
    • On directed paths and circuits
    • P. Erdos, G. Katona (Eds.), Academic Press, New York, NY
    • T. Gallai, On directed paths and circuits, in: P. Erdos, G. Katona (Eds.), Theory of Graphs, Academic Press, New York, NY, 1968, pp. 115-118.
    • (1968) Theory of Graphs , pp. 115-118
    • Gallai, T.1
  • 30
    • 0004249508 scopus 로고
    • North-Holland, Amsterdam, The Netherlands
    • C. Berge, Graphs and Hypergraphs, North-Holland, Amsterdam, The Netherlands, 1976.
    • (1976) Graphs and Hypergraphs
    • Berge, C.1
  • 31
    • 0010314031 scopus 로고    scopus 로고
    • Generating all the acyclic orientations of an undirected graph
    • V.C. Barbosa, J.L. Szwarcfiter, Generating all the acyclic orientations of an undirected graph, Inform. Process. Lett. 72 (1999) 71-74.
    • (1999) Inform. Process. Lett. , vol.72 , pp. 71-74
    • Barbosa, V.C.1    Szwarcfiter, J.L.2
  • 34
    • 3543135390 scopus 로고    scopus 로고
    • Two novel evolutionary formulations of the graph coloring problem
    • V.C. Barbosa, C.A.G. Assis, J.O. do Nascimento, Two novel evolutionary formulations of the graph coloring problem, J. Combin. Optim. 8 (2004) 41-63.
    • (2004) J. Combin. Optim. , vol.8 , pp. 41-63
    • Barbosa, V.C.1    Assis, C.A.G.2    Do Nascimento, J.O.3
  • 35
    • 0024749885 scopus 로고
    • Concurrency in heavily loaded neighborhood-constrained systems
    • V.C. Barbosa, E. Gafni, Concurrency in heavily loaded neighborhood-constrained systems, ACM Trans. Progr. Lang. Systems 11 (1989) 562-584.
    • (1989) ACM Trans. Progr. Lang. Systems , vol.11 , pp. 562-584
    • Barbosa, V.C.1    Gafni, E.2
  • 37
    • 4544303082 scopus 로고    scopus 로고
    • The interleaved multichromatic number of a graph
    • V.C. Barbosa, The interleaved multichromatic number of a graph, Ann. Combin. 6 (2002) 249-256.
    • (2002) Ann. Combin. , vol.6 , pp. 249-256
    • Barbosa, V.C.1
  • 38
    • 0035805828 scopus 로고    scopus 로고
    • Optimization with extremal dynamics
    • S. Boettcher, A.G. Percus, Optimization with extremal dynamics, Phys. Rev. Lett. 86 (2001) 5211-5214.
    • (2001) Phys. Rev. Lett. , vol.86 , pp. 5211-5214
    • Boettcher, S.1    Percus, A.G.2
  • 40
    • 4544383272 scopus 로고    scopus 로고
    • D.S. Johnson, ftp://dimacs.rutgers.edu/pub/dsj/clique/dfmax.c.
    • Johnson, D.S.1
  • 41
    • 0025521978 scopus 로고
    • An exact algorithm for the maximum clique problem
    • R. Carraghan, P.M. Pardalos, An exact algorithm for the maximum clique problem, Oper. Res. Lett. 9 (1990) 375-382.
    • (1990) Oper. Res. Lett. , vol.9 , pp. 375-382
    • Carraghan, R.1    Pardalos, P.M.2
  • 42
    • 0038438594 scopus 로고    scopus 로고
    • On the number of maximal independent sets in a graph
    • BRICS, Department of Computer Science, University of Aarhus, Aarhus, Denmark, April
    • J.M. Nielsen, On the number of maximal independent sets in a graph, Technical Report BRICS RS-02-15, BRICS, Department of Computer Science, University of Aarhus, Aarhus, Denmark, April 2002.
    • (2002) Technical Report , vol.BRICS RS-02-15
    • Nielsen, J.M.1
  • 44
    • 0001387789 scopus 로고
    • A decomposition theorem for partially ordered sets
    • R.P. Dilworth, A decomposition theorem for partially ordered sets, Ann. Math. 51 (1950) 161-165.
    • (1950) Ann. Math. , vol.51 , pp. 161-165
    • Dilworth, R.P.1
  • 46
    • 0000122499 scopus 로고    scopus 로고
    • On implementing push-relabel method for the maximum flow problem
    • B.V. Cherkassky, A.V. Goldberg, On implementing push-relabel method for the maximum flow problem, Algorithmica 19 (1997) 390-410.
    • (1997) Algorithmica , vol.19 , pp. 390-410
    • Cherkassky, B.V.1    Goldberg, A.V.2
  • 47
    • 4544286108 scopus 로고    scopus 로고
    • A novel evolutionary formulation of the maximum independent set problem
    • COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil, September
    • V.C. Barbosa, L.C.D. Campos, A novel evolutionary formulation of the maximum independent set problem, Technical Report ES-615/03, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil, September 2003.
    • (2003) Technical Report , vol.ES-615-03
    • Barbosa, V.C.1    Campos, L.C.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.