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Volumn 46, Issue 3, 2004, Pages 167-179

Some probabilistic restatements of the four color conjecture

Author keywords

Four Color Conjecture; Graph polynomial; Tait coloring

Indexed keywords

COLOR; CORRELATION METHODS; GRAPH THEORY; POLYNOMIALS; RANDOM PROCESSES; THEOREM PROVING;

EID: 3042523213     PISSN: 03649024     EISSN: None     Source Type: Journal    
DOI: 10.1002/jgt.10178     Document Type: Article
Times cited : (7)

References (22)
  • 1
    • 0039527934 scopus 로고    scopus 로고
    • A note on graph colorings and graph polynomials
    • N. Alon and M. Tarsi, A note on graph colorings and graph polynomials, J Combin Theory B 70 (1997), 197-201.
    • (1997) J Combin Theory B , vol.70 , pp. 197-201
    • Alon, N.1    Tarsi, M.2
  • 2
    • 84972498411 scopus 로고
    • Every planar map is four colorable. Part I. Discharging
    • K. Appel and W. Haken, Every planar map is four colorable. Part I. Discharging, Illinois J Mathematics 21 (1977), 429-490.
    • (1977) Illinois J Mathematics , vol.21 , pp. 429-490
    • Appel, K.1    Haken, W.2
  • 3
    • 84972500815 scopus 로고
    • Every planar map is four colorable. Part II. Reducibility
    • K. Appel, W. Haken, and J. Koch, Every planar map is four colorable. Part II. Reducibility, Illinois J Mathematics 21 (1977), 491-567.
    • (1977) Illinois J Mathematics , vol.21 , pp. 491-567
    • Appel, K.1    Haken, W.2    Koch, J.3
  • 4
    • 0003199706 scopus 로고
    • Every planar map is four colorable
    • Amer Math Soc Providence, RI
    • K. Appel and W. Haken, Every planar map is four colorable, AMS Contemporary Mathematics, 98, Amer Math Soc Providence, RI, 1989.
    • (1989) AMS Contemporary Mathematics , vol.98
    • Appel, K.1    Haken, W.2
  • 5
    • 0001318040 scopus 로고
    • On a new graph invariant and a criterion for planarity
    • Amer Math Soc Providence, RI
    • Yves Colin de Verdiere, On a new graph invariant and a criterion for planarity, AMS Contemporary Mathematics, 147, Amer Math Soc Providence, RI, 1993.
    • (1993) AMS Contemporary Mathematics , vol.147
    • De Verdiere, Y.C.1
  • 8
    • 0004478475 scopus 로고
    • Is the four color theorem true?
    • P. C. Kainen, Is the four color theorem true?, Geombinatorics 3 (1993), 41-56.
    • (1993) Geombinatorics , vol.3 , pp. 41-56
    • Kainen, P.C.1
  • 9
    • 38249020702 scopus 로고
    • Map coloring and the vector cross product
    • L. Kaufmann, Map coloring and the vector cross product, J Combin Theory B 48 (1990), 145-154.
    • (1990) J Combin Theory B , vol.48 , pp. 145-154
    • Kaufmann, L.1
  • 10
    • 0004505662 scopus 로고
    • Combinatorial recoupling theory and 3-manifold invariants. Low-dimensional topology and quantum field theory
    • Cambridge, Plenum, New York
    • L. H. Kauffman, Combinatorial recoupling theory and 3-manifold invariants. Low-dimensional topology and quantum field theory (Cambridge, 1992), (NATO Adv Sci Inst Ser B Phys, 315), Plenum, New York, 1993, pp. 1-17.
    • (1992) NATO Adv Sci Inst Ser B Phys , vol.315 , pp. 1-17
    • Kauffman, L.H.1
  • 11
    • 0004520266 scopus 로고
    • Spin networks, topology and discrete physics
    • World Sei Publishing, River Edge, NJ
    • L. H. Kauffman, Spin networks, topology and discrete physics, Adv Ser Math Phys 17, World Sei Publishing, River Edge, NJ, 1994, 234-274.
    • (1994) Adv Ser Math Phys , vol.17 , pp. 234-274
    • Kauffman, L.H.1
  • 12
    • 21144472490 scopus 로고
    • An algebraic approach to the planar coloring problem
    • L. H. Kauffman and H. Saleur, An algebraic approach to the planar coloring problem, Commun Math Phy 152 (1993), 565-590.
    • (1993) Commun Math Phy , vol.152 , pp. 565-590
    • Kauffman, L.H.1    Saleur, H.2
  • 13
    • 3042692805 scopus 로고
    • in Russian, Combinatorial and asymptotical analysis, G. P. Egorychev (Editor), Krasnoyarskii State University, Krasnoyarsk; MR 58 #27504, ZB1 431, 00010
    • Yu. Matiyasevich, Problem 21 (in Russian), Combinatorial and asymptotical analysis, issue 2, G. P. Egorychev (Editor), Krasnoyarskii State University, Krasnoyarsk, 1977, pp. 178-179; MR 58 #27504, ZB1 431, 00010.
    • (1977) Problem , vol.21 , Issue.2 , pp. 178-179
    • Matiyasevich, Yu.1
  • 14
    • 0004476190 scopus 로고    scopus 로고
    • Mirrored at: http://www.informatik.uni-stuttgart.de/ ifi/ti/personen/ Matiyasevich/Journal/Triangular/triang.htm
    • Yu. Matiyasevich, A polynomial related to colourings of triangulation of sphere. Available at: URL: http://logic.pdmi.ras.ru/~yumat/Journal/ Triangular/triang.htm. Mirrored at: http://www.informatik.uni-stuttgart.de/ ifi/ti/personen/Matiyasevich/Journal/Triangular/triang.htm.
    • A Polynomial Related to Colourings of Triangulation of Sphere
    • Matiyasevich, Yu.1
  • 15
    • 0034923603 scopus 로고    scopus 로고
    • Some arithmetical restatements of the four color conjecture
    • mirrored at http://www.informatik.uni-stuttgart.de/ifi/ti/ personen/Matiyasevich/Journal/jcontord.htm)
    • Yu. Matiyasevich, Some arithmetical restatements of the four color conjecture, Theoretical Computer Sci 257 (2001), 167-183 (a version of this paper is available via URL: http://logic.pdmi.ras.ru/~yumat/Journal/ jcontord.htm, mirrored at http://www.informatik.uni-stuttgart.de/ifi/ti/ personen/Matiyasevich/Journal/jcontord.htm).
    • (2001) Theoretical Computer Sci , vol.257 , pp. 167-183
    • Matiyasevich, Yu.1
  • 16
    • 3042694970 scopus 로고    scopus 로고
    • Some algebraic methods for calculation of the number of colorings of a graph
    • in Russian
    • Yu. V. Matiyasevich, Some algebraic methods for calculation of the number of colorings of a graph (in Russian), Zapiski Nauchnykh Seminarov POMI 283 (2001), 193-205 (available via URL http://www.pdmi.ras.ru/znsl/2001/ v283.html).
    • (2001) Zapiski Nauchnykh Seminarov POMI , vol.283 , pp. 193-205
    • Matiyasevich, Yu.V.1
  • 17
    • 3042546999 scopus 로고    scopus 로고
    • A probabilistic equivalent to the four color conjecture
    • in Russian
    • Yu. V. Matiyasevich, A probabilistic equivalent to the four color conjecture (in Russian), Teoriya Veroyatnostei i ee Primeneniya 48 (2003), 411-416.
    • (2003) Teoriya Veroyatnostei i ee Primeneniya , vol.48 , pp. 411-416
    • Matiyasevich, Yu.V.1
  • 18
  • 20
    • 0000189235 scopus 로고    scopus 로고
    • An update on the four-colour theorem
    • R. Thomas, An update on the four-colour theorem, Notices of the AMS 45 (1998), 848-859 (available via URLs: http://www.ams.org/noticies/199807/ thomas.{ps,pdf}).
    • (1998) Notices of the AMS , vol.45 , pp. 848-859
    • Thomas, R.1
  • 21
    • 0001835934 scopus 로고
    • Thirteen colorful variations on Guthrie's four-color conjecture
    • T. L. Saaty, Thirteen colorful variations on Guthrie's four-color conjecture, Am Mathematical Monthly 79 (1972), 2-43.
    • (1972) Am Mathematical Monthly , vol.79 , pp. 2-43
    • Saaty, T.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.