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Volumn 21, Issue 3, 1977, Pages 429-490

Every planar map is four colorable part I: Discharging1

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EID: 84972498411     PISSN: 00192082     EISSN: None     Source Type: Journal    
DOI: 10.1215/ijm/1256049011     Document Type: Article
Times cited : (780)

References (30)
  • 2
    • 84972539146 scopus 로고    scopus 로고
    • A systematic approach to the determination of reducible configurations in the four-color conjecture
    • to appear
    • F. Allaire and E. R. Swart, A systematic approach to the determination of reducible configurations in the four-color conjecture, J. Combinatorial Theory (B), to appear.
    • J. Combinatorial Theory (B)
    • Allaire, F.1    Swart, E.R.2
  • 3
    • 84972542546 scopus 로고    scopus 로고
    • An unavoidable set of configurations in planar triangulations
    • to appear
    • K. Appel and W. Haken, An unavoidable set of configurations in planar triangulations, J. Combinatorial Theory (B), to appear.
    • J. Combinatorial Theory (B)
    • Appel, K.1    Haken, W.2
  • 4
    • 84972507664 scopus 로고
    • The existence of unavoidable sets of geographically good configurations
    • K. Appel and W. Haken, The existence of unavoidable sets of geographically good configurations, Illinois J. Math., vol. 20 (1976), pp. 218-297.
    • (1976) Illinois J. Math. , vol.20 , pp. 218-297
    • Appel, K.1    Haken, W.2
  • 6
    • 0041978402 scopus 로고
    • Six rings in minimal five color maps
    • A. Bernhart, Six rings in minimal five color maps, Amer. J. Math., vol. 69 (1947), pp. 391-412.
    • (1947) Amer. J. Math. , vol.69 , pp. 391-412
    • Bernhart, A.1
  • 7
    • 0010963110 scopus 로고
    • Another reducible edge configuration
    • A. Bernhart, Another reducible edge configuration, Amer. J. Math., vol. 70 (1948), pp. 144-146.
    • (1948) Amer. J. Math. , vol.70 , pp. 144-146
    • Bernhart, A.1
  • 8
    • 84972503141 scopus 로고    scopus 로고
    • On the characterization of reductions of small order
    • to appear
    • F. Bernhart, On the characterization of reductions of small order, J. Combinatorial Theory (B), to appear.
    • J. Combinatorial Theory (B)
    • Bernhart, F.1
  • 10
    • 0003292275 scopus 로고
    • The reducibility of maps
    • G. D. Birkhoff, The reducibility of maps, Amer. J. Math., vol. 35 (1913), pp. 114-128.
    • (1913) Amer. J. Math. , vol.35 , pp. 114-128
    • Birkhoff, G.D.1
  • 11
    • 84910184862 scopus 로고
    • A contribution to the four color problem
    • C. Chojnacki, A contribution to the four color problem, Amer. J. Math., vol. 64 (1942), pp. 36-54.
    • (1942) Amer. J. Math. , vol.64 , pp. 36-54
    • Chojnacki, C.1
  • 13
    • 84910205344 scopus 로고
    • Une contribution au problème des quatre couleurs
    • P. Errera, Une contribution au problème des quatre couleurs, Bull. Soc. Math. France, vol. 53 (1925), pp. 42-55.
    • (1925) Bull. Soc. Math. France , vol.53 , pp. 42-55
    • Errera, P.1
  • 14
    • 0039887149 scopus 로고
    • The four color problem
    • Ph. Franklin, The four color problem, Amer. J. Math., vol. 44 (1922), pp. 225-236.
    • (1922) Amer. J. Math. , vol.44 , pp. 225-236
    • Franklin, P.1
  • 15
    • 49549162567 scopus 로고
    • An existence theorem for planar maps
    • W. Haken, An existence theorem for planar maps, J. Combinatorial Theory, vol. 14 (1973), pp. 180-184.
    • (1973) J. Combinatorial Theory , vol.14 , pp. 180-184
    • Haken, W.1
  • 16
    • 0011002456 scopus 로고
    • I-Hochschulscripten 810/810a/810b, Bibliographisches Institut, Mannheim/Vienna/Zurich
    • H. Heesch, Untersuchungen zum Vierfarbenproblem, I-Hochschulscripten 810/810a/810b, Bibliographisches Institut, Mannheim/Vienna/Zurich, 1969.
    • (1969) Untersuchungen zum Vierfarbenproblem
    • Heesch, H.1
  • 19
    • 0000291982 scopus 로고
    • On the geographical problem of the four colors
    • A. B. Kempe, On the geographical problem of the four colors, Amer. J. Math., vol. 2 (1879), pp. 193-200.
    • (1879) Amer. J. Math. , vol.2 , pp. 193-200
    • Kempe, A.B.1
  • 20
    • 84972491151 scopus 로고
    • Ph.D. Thesis, Department of Com puter Science Report no. UIUCDCS-R-76-802, University of Illinois at Urbana-Champaign, Urbana, Illinois
    • J. Koch, Computation of four color reducibility, Ph.D. Thesis, 1976, Department of Com puter Science Report no. UIUCDCS-R-76-802, University of Illinois at Urbana-Champaign, Urbana, Illinois.
    • (1976) Computation of four color reducibility
    • Koch, J.1
  • 21
    • 0002354109 scopus 로고
    • Quelques conséquences simples de la Formule d’Euler
    • H. Lebesgue, Quelques conséquences simples de la Formule d’Euler, J. de Math., vol. 9 (1940), pp. 27-43.
    • (1940) J. de Math. , vol.9 , pp. 27-43
    • Lebesgue, H.1
  • 22
    • 84972491165 scopus 로고    scopus 로고
    • Problème des quatre couleurs, un contre-exemple doit avoir au moins 96 sommets
    • to appear
    • J. Mayer, Problème des quatre couleurs, un contre-exemple doit avoir au moins 96 sommets, J. Combinatorial Theory (B), to appear.
    • J. Combinatorial Theory (B)
    • Mayer, J.1
  • 23
    • 0040480003 scopus 로고
    • Numerical calculations on the four color problem
    • O. Ore and J. Stemple, Numerical calculations on the four color problem, J. Combinatorial Theory, vol. 8 (1970), pp. 65-78.
    • (1970) J. Combinatorial Theory , vol.8 , pp. 65-78
    • Ore, O.1    Stemple, J.2
  • 25
    • 84910242770 scopus 로고
    • Doctoral Dissertation, Technische Universität Hannover
    • R. Stanik, Zur Reduction von Triangulationen, Doctoral Dissertation, Technische Universität Hannover, 1974.
    • (1974) Zur Reduction von Triangulationen
    • Stanik, R.1
  • 27
    • 0039887087 scopus 로고
    • Kempe chains and the four colour problem
    • reprinted in Studies in Graph Theory, Studies in Math., Math. Assoc, of America, vol. 12, 1976
    • W. Tutte and H. Whitney, Kempe chains and the four colour problem, Utilitas Math ematica, vol. 2 (1972), pp. 241-281, reprinted in Studies in Graph Theory, Studies in Math., Math. Assoc, of America, vol. 12, 1976.
    • (1972) Utilitas Math ematica , vol.2 , pp. 241-281
    • Tutte, W.1    Whitney, H.2
  • 28
    • 0040889316 scopus 로고
    • Über den kartographischen Vierfarbensatz
    • P. Wernicke, Über den kartographischen Vierfarbensatz, Math. Ann., vol. 58 (1904), pp. 413-426.
    • (1904) Math. Ann. , vol.58 , pp. 413-426
    • Wernicke, P.1
  • 29
    • 84910214387 scopus 로고
    • On the minimum number of polygons in an irreducible map
    • C. Winn, On the minimum number of polygons in an irreducible map, Amer. J. Math., vol. 62 (1940), pp. 406-416.
    • (1940) Amer. J. Math. , vol.62 , pp. 406-416
    • Winn, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.