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Volumn 67, Issue 1, 1996, Pages 34-47

Snarks without small cycles

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EID: 0030141041     PISSN: 00958956     EISSN: None     Source Type: Journal    
DOI: 10.1006/jctb.1996.0032     Document Type: Article
Times cited : (83)

References (34)
  • 2
    • 51249183693 scopus 로고
    • The sextet construction for cubic graphs
    • 2. N. L. BIGGS AND M. J. HOARE, The sextet construction for cubic graphs, Combinatorica 3 (1983), 153-165.
    • (1983) Combinatorica , vol.3 , pp. 153-165
    • Biggs, N.L.1    Hoare, M.J.2
  • 5
    • 0011693355 scopus 로고
    • Ph.D. thesis, Dept. of Combinatorics and Optimization, University of Waterloo, Canada
    • 5. U. A. CELMINS, On cubic graphs that do not have an edge-3-colouring, Ph.D. thesis, Dept. of Combinatorics and Optimization, University of Waterloo, Canada, 1984.
    • (1984) On Cubic Graphs That Do Not Have An Edge-3-colouring
    • Celmins, U.A.1
  • 6
    • 0004185082 scopus 로고
    • Research Report CORR 79-18, Dept. of Combinatorics and Optimization, University of Waterloo, Canada
    • 6. U. A. CELMINS AND E. R. SWART, "The Construction of Snarks," Research Report CORR 79-18, Dept. of Combinatorics and Optimization, University of Waterloo, Canada, 1979.
    • (1979) The Construction of Snarks
    • Celmins, U.A.1    Swart, E.R.2
  • 7
    • 0001135194 scopus 로고
    • Snarks and supersnarks
    • G. Chartrand. Y. Alavi, D. L. Goldsmith, L. Lesniak-Foster, D. R. Lick, Eds., Wiley, New York
    • 7. A. G. CHETWYND AND R. J. WILSON, Snarks and supersnarks, in "The Theory and Applications of Graphs" (G. Chartrand. Y. Alavi, D. L. Goldsmith, L. Lesniak-Foster, D. R. Lick, Eds.), pp. 215-241, Wiley, New York, 1981.
    • (1981) The Theory and Applications of Graphs , pp. 215-241
    • Chetwynd, A.G.1    Wilson, R.J.2
  • 8
    • 0011632451 scopus 로고
    • Network coloring
    • 8. B. DESCARTES, Network coloring, Math. Gazette 32 (1948), 67-69.
    • (1948) Math. Gazette , vol.32 , pp. 67-69
    • Descartes, B.1
  • 9
    • 0000471093 scopus 로고
    • Reguläre graphen gegebener taillenweite mit minimaler knotenzahl
    • 9. P. ERDOS AND H. SACHS, Reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl, Wis. Z. Univ. Halle-Wittenberg, Math.-Nat. R. 12 (1963), 251-258.
    • (1963) Wis. Z. Univ. Halle-Wittenberg, Math.-Nat. R. , vol.12 , pp. 251-258
    • Erdos, P.1    Sachs, H.2
  • 10
    • 0011572854 scopus 로고
    • A Boolean algebra approach to the construction of sparks
    • Y. Alavi, G. Chartrand, O. R. Oellermann, A. J. Shwenk, Eds., Wiley, New York
    • 10. M. A. FIOL, A Boolean algebra approach to the construction of sparks, in "Graph Theory, Combinatorics, and Applications" (Y. Alavi, G. Chartrand, O. R. Oellermann, A. J. Shwenk, Eds.), pp. 493-524, Wiley, New York, 1991.
    • (1991) Graph Theory, Combinatorics, and Applications , pp. 493-524
    • Fiol, M.A.1
  • 11
    • 0011619520 scopus 로고
    • Mathematical games: Snarks, boojums, and other conjectures related to the four-color-map theorem
    • April
    • 11. M. GARDNER, Mathematical games: Snarks, boojums, and other conjectures related to the four-color-map theorem, Sci. Am. 234, April (1976), 126-130.
    • (1976) Sci. Am. , vol.234 , pp. 126-130
    • Gardner, M.1
  • 12
    • 0011632868 scopus 로고
    • A girth requirement for the double cycle cover conjecture
    • "Cycles in Graphs" (B. R. Alspach and C. D. Godsil, Eds.), North-Holland, Amsterdam
    • 12. L. GODDYN, A girth requirement for the double cycle cover conjecture, in "Cycles in Graphs" (B. R. Alspach and C. D. Godsil, Eds.), Ann. Discrete Math., Vol. 27, pp. 13-26, North-Holland, Amsterdam, 1985.
    • (1985) Ann. Discrete Math. , vol.27 , pp. 13-26
    • Goddyn, L.1
  • 13
    • 51249183654 scopus 로고
    • Explicit construction of regular graphs without small cycles
    • 13. W. IMRICH, Explicit construction of regular graphs without small cycles, Combinatorica 4 (1984), 53-59.
    • (1984) Combinatorica , vol.4 , pp. 53-59
    • Imrich, W.1
  • 14
    • 0001634441 scopus 로고
    • Infinite families of non-trivial trivalent graphs which are not Tait colorable
    • 14. R. ISAACS, Infinite families of non-trivial trivalent graphs which are not Tait colorable, Amer. Math. Monthly 82 (1975), 221-239.
    • (1975) Amer. Math. Monthly , vol.82 , pp. 221-239
    • Isaacs, R.1
  • 15
    • 0011636424 scopus 로고
    • A survey of the cycle double cover conjecture
    • "Cycles in Graphs" (B. R. Alspach and C. D. Godsil, Eds.), North-Holland, Amsterdam
    • 15. F. JAEGER, A survey of the cycle double cover conjecture, in "Cycles in Graphs" (B. R. Alspach and C. D. Godsil, Eds.), Ann. Discrete Math., Vol. 27, pp. 1-12, North-Holland, Amsterdam, 1985.
    • (1985) Ann. Discrete Math. , vol.27 , pp. 1-12
    • Jaeger, F.1
  • 16
    • 0002166337 scopus 로고
    • Nowhere-zero flow problems
    • L. Beineke and R. J. Wilson, Eds., Academic Press, New York
    • 16. F. JAEGER, Nowhere-zero flow problems, in "Selected topics in Graph Theory 3" (L. Beineke and R. J. Wilson, Eds.), pp. 71-95, Academic Press, New York, 1988.
    • (1988) Selected Topics in Graph Theory 3 , vol.3 , pp. 71-95
    • Jaeger, F.1
  • 17
    • 0001501637 scopus 로고
    • Conjecture 1
    • "Combinatorics 79" (M. Deza and I. G. Rosenberg, Eds.), Problem Session, North-Holland, Amsterdam
    • 17. F. JAEGER AND T. SWART, Conjecture 1, in "Combinatorics 79" (M. Deza and I. G. Rosenberg, Eds.), Ann. Discrete Math., Vol. 9, p. 305, Problem Session, North-Holland, Amsterdam, 1980.
    • (1980) Ann. Discrete Math. , vol.9 , pp. 305
    • Jaeger, F.1    Swart, T.2
  • 18
    • 0001501637 scopus 로고
    • Conjecture 2
    • "Combinatorics 79" (M. Deza and I. G. Rosenberg, Eds.), Problem Session, North-Holland, Amsterdam
    • 18. F. JAEGER AND T. SWART, Conjecture 2, in "Combinatorics 79" (M. Deza and I. G. Rosenberg, Eds.), Ann. Discrete Math., Vol. 9, p. 305, Problem Session, North-Holland, Amsterdam, 1980.
    • (1980) Ann. Discrete Math. , vol.9 , pp. 305
    • Jaeger, F.1    Swart, T.2
  • 19
    • 0346751074 scopus 로고    scopus 로고
    • Constructing regular maps and graphs from planar quotients
    • submitted
    • 19. S. JENDROL', R. NEDELA, AND M. Škoviera, Constructing regular maps and graphs from planar quotients, Math. Slovaca, submitted.
    • Math. Slovaca
    • Jendrol', S.1    Nedela, R.2    Škoviera, M.3
  • 20
    • 85029967720 scopus 로고    scopus 로고
    • A cyclically 6-edge-connected snark of order 118
    • to appear
    • 20. M. KOCHOL, A cyclically 6-edge-connected snark of order 118, Discrete Math., to appear.
    • Discrete Math.
    • Kochol, M.1
  • 21
    • 0011633191 scopus 로고
    • Technical Report TR-II-SAS-07/93-5, Institute for Informatics, Slovak Academy of Sciences, Bratislava, Slovakia
    • 21. M. KOCHOL, "Construction of Cyclically 6-Edge-Connected Snarks," Technical Report TR-II-SAS-07/93-5, Institute for Informatics, Slovak Academy of Sciences, Bratislava, Slovakia, 1993.
    • (1993) Construction of Cyclically 6-Edge-Connected Snarks
    • Kochol, M.1
  • 23
    • 0003059022 scopus 로고
    • Javnyje teoretiko-grupovyje konstrukcii kombinatornych schem i ich primenenija v postroenii rasširitelej i koncentratorov
    • 23. G. A. MARGULIS, Javnyje teoretiko-grupovyje konstrukcii kombinatornych schem i ich primenenija v postroenii rasširitelej i koncentratorov, Problemy Peredači Informacii 24 (1988), 51-60.
    • (1988) Problemy Peredači Informacii , vol.24 , pp. 51-60
    • Margulis, G.A.1
  • 24
    • 0000113462 scopus 로고
    • A minimal cubic graph of girth seven
    • 24. W. F. MCGEE, A minimal cubic graph of girth seven, Canad. Math. Bull. 3 (1960), 149-152.
    • (1960) Canad. Math. Bull. , vol.3 , pp. 149-152
    • McGee, W.F.1
  • 25
    • 0011567035 scopus 로고
    • Atoms of cyclic connectivity in transitive cubic graphs
    • R. Bodendiek, Ed., BI-Wissenschaftsverlag, Mannheim
    • 25. R. NEDELA AND M. ŠKOVIERA, Atoms of cyclic connectivity in transitive cubic graphs, in "Contemporary Methods in Graph Theory" (R. Bodendiek, Ed.), pp. 470-488, BI-Wissenschaftsverlag, Mannheim, 1990.
    • (1990) Contemporary Methods in Graph Theory , pp. 470-488
    • Nedela, R.1    Škoviera, M.2
  • 27
    • 0011674362 scopus 로고
    • Remarks on the colouring of maps
    • 27. P. G. TAIT, Remarks on the colouring of maps, Proc. R. Soc. Edinburgh 10 (1880), 501-503, 729.
    • (1880) Proc. R. Soc. Edinburgh , vol.10 , pp. 501-503
    • Tait, P.G.1
  • 28
    • 0002092950 scopus 로고
    • A contribution to the theory of chromatic polynomials
    • 28. W. T. TUTTE, A contribution to the theory of chromatic polynomials, Canad. J. Math. 6 (1954), 80-91.
    • (1954) Canad. J. Math. , vol.6 , pp. 80-91
    • Tutte, W.T.1
  • 29
    • 0002055748 scopus 로고
    • On the algebraic theory of graph colorings
    • 29. W. T. TUTTE, On the algebraic theory of graph colorings, J. Combin. Theory 1 (1966), 15-50.
    • (1966) J. Combin. Theory , vol.1 , pp. 15-50
    • Tutte, W.T.1
  • 30
    • 0002935868 scopus 로고
    • On an estimate of the chromatic class of a p-graph
    • 30. V. G. VIZING, On an estimate of the chromatic class of a p-graph, Diskret. Analiz 3 (1964), 25-30.
    • (1964) Diskret. Analiz , vol.3 , pp. 25-30
    • Vizing, V.G.1
  • 31
    • 0011631851 scopus 로고
    • Über reguläre graphen gegebener taillenweite mit minimaler knotenzahl
    • 31. H. WALTHER, Über reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl, Wiss. Z. HfE Ilmenau 11 (1965), 93-96.
    • (1965) Wiss. Z. HfE Ilmenau , vol.11 , pp. 93-96
    • Walther, H.1
  • 32
    • 0011631851 scopus 로고
    • Eigenschaften van regulären graphen gegebener taillenweite mit minimaler knotenzahl
    • 32. H. WALTHER, Eigenschaften van regulären Graphen gegebener Taillenweite mit minimaler Knotenzahl, Wiss. Z. HfE Ilmenau 11 (1965), 167-168.
    • (1965) Wiss. Z. HfE Ilmenau , vol.11 , pp. 167-168
    • Walther, H.1
  • 33
    • 0002978601 scopus 로고
    • A survey of snarks
    • Y. Alavi, G. Chartrand, O. R. Oellermann, and A. J. Schwenk, Eds., Wiley, New York
    • 33. J. J. WATKINS AND R. J. WILSON, A survey of snarks, in "Graph Theory, Combinatorics, and Applications" (Y. Alavi, G. Chartrand, O. R. Oellermann, and A. J. Schwenk, Eds.), pp. 1129-1144, Wiley, New York, 1991.
    • (1991) Graph Theory, Combinatorics, and Applications , pp. 1129-1144
    • Watkins, J.J.1    Wilson, R.J.2
  • 34
    • 51249180859 scopus 로고
    • Girths of bipartite sextet graphs
    • 34. A. WEISS, Girths of bipartite sextet graphs, Combinatorica 4 (1984), 241-245.
    • (1984) Combinatorica , vol.4 , pp. 241-245
    • Weiss, A.1


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