Hypohamiltonian graph (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Hypohamiltonian graph" in English language version.

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Thomassen (1981). Thomassen, Carsten (1981), "Planar cubic hypo-Hamiltonian and hypotraceable graphs", Journal of Combinatorial Theory, Series B, 30: 36–44, doi:10.1016/0095-8956(81)90089-7, MR 0609592.
The existence of planar hypohamiltonian graphs was posed as an open question by Chvátal (1973), and Chvátal, Klarner & Knuth (1972) offered a $5 prize for the construction of one. Thomassen (1976) used Grinberg's theorem to find planar hypohamiltonian graphs of girth 3, 4, and 5 and showed that there exist infinitely many planar hypohamiltonian graphs. Chvátal, V. (1973), "Flip-flops in hypo-Hamiltonian graphs", Canadian Mathematical Bulletin, 16: 33–41, doi:10.4153/CMB-1973-008-9, MR 0371722. Chvátal, V.; Klarner, D. A.; Knuth, D. E. (1972), Selected Combinatorial Research Problems (PDF), Tech. Report STAN-CS-72-292, Computer Science Department, Stanford University. Thomassen, Carsten (1976), "Planar and infinite hypohamiltonian and hypotraceable graphs", Discrete Mathematics, 14 (4): 377–389, doi:10.1016/0012-365X(76)90071-6, MR 0422086.
Jooyandeh et al. (2017), using a computer search and Grinberg's theorem. Earlier small planar hypohamiltonian graphs with 42, 57 and 48 vertices, respectively, were found by Wiener & Araya (2009), Hatzel (1979) and Zamfirescu & Zamfirescu (2007). Jooyandeh, Mohammadreza; McKay, Brendan D.; Östergård, Patric R. J.; Pettersson, Ville H.; Zamfirescu, Carol T. (2017), "Planar Hypohamiltonian Graphs on 40 Vertices", Journal of Graph Theory, 84 (2): 121–133, arXiv:1302.2698, Bibcode:2013arXiv1302.2698J, doi:10.1002/jgt.22015. Wiener, Gábor; Araya, Makoto (2009), The ultimate question, arXiv:0904.3012, Bibcode:2009arXiv0904.3012W. Hatzel, W. (1979), "Ein planarer hypohamiltonscher Graph mit 57 Knoten", Math. Ann., 243 (3): 213–216, doi:10.1007/BF01424541, MR 0548801, S2CID 121794449. Zamfirescu, C. T.; Zamfirescu, T. I. (2007), "A planar hypohamiltonian graph with 48 vertices", Journal of Graph Theory, 55 (4): 338–342, doi:10.1002/jgt.20241.
Thomassen (1978). Thomassen, Carsten (1978), "Hypohamiltonian graphs and digraphs", Theory and applications of graphs (Proc. Internat. Conf., Western Mich. Univ., Kalamazoo, Mich., 1976), Lecture Notes in Mathematics, vol. 642, Berlin: Springer-Verlag, pp. 557–571, MR 0499523.
Steffen (1998); Steffen (2001). Steffen, E. (1998), "Classification and characterizations of snarks", Discrete Mathematics, 188 (1–3): 183–203, doi:10.1016/S0012-365X(97)00255-0, MR 1630478. Steffen, E. (2001), "On bicritical snarks", Math. Slovaca, 51 (2): 141–150, MR 1841443.
Collier & Schmeichel (1977). Collier, J. B.; Schmeichel, E. F. (1977), "New flip-flop constructions for hypohamiltonian graphs", Discrete Mathematics, 18 (3): 265–271, doi:10.1016/0012-365X(77)90130-3, MR 0543828.
Robertson (1969) proved that these graphs are non-Hamiltonian, while it is straightforward to verify that their one-vertex deletions are Hamiltonian. See Alspach (1983) for a classification of non-Hamiltonian generalized Petersen graphs. Robertson, G. N. (1969), Graphs minimal under girth, valency and connectivity constraints, Ph. D. thesis, Waterloo, Ontario: University of Waterloo. Alspach, B. R. (1983), "The classification of Hamiltonian generalized Petersen graphs", Journal of Combinatorial Theory, Series B, 34 (3): 293–312, doi:10.1016/0095-8956(83)90042-4, MR 0714452.
Thomassen (1974a); Doyen & van Diest (1975). Thomassen, Carsten (1974a), "Hypohamiltonian and hypotraceable graphs", Discrete Mathematics, 9: 91–96, doi:10.1016/0012-365X(74)90074-0, MR 0347682. Doyen, J.; van Diest, V. (1975), "New families of hypohamiltonian graphs", Discrete Mathematics, 13 (3): 225–236, doi:10.1016/0012-365X(75)90020-5, MR 0416979.
Kapoor, Kronk & Lick (1968); Kronk (1969); Grünbaum (1974); Thomassen (1974a). Kapoor, S. F.; Kronk, H. V.; Lick, D. R. (1968), "On detours in graphs", Canadian Mathematical Bulletin, 11 (2): 195–201, doi:10.4153/CMB-1968-022-8, MR 0229543. Kronk, H. V. (1969), Klee, V. (ed.), "Does there exist a hypotraceable graph?", Research Problems, American Mathematical Monthly, 76 (7): 809–810, doi:10.2307/2317879, JSTOR 2317879. Grünbaum, B. (1974), "Vertices missed by longest paths or circuits", Journal of Combinatorial Theory, Series A, 17: 31–38, doi:10.1016/0097-3165(74)90025-9, MR 0349474. Thomassen, Carsten (1974a), "Hypohamiltonian and hypotraceable graphs", Discrete Mathematics, 9: 91–96, doi:10.1016/0012-365X(74)90074-0, MR 0347682.
Fouquet & Jolivet (1978); Grötschel & Wakabayashi (1980); Grötschel & Wakabayashi (1984); Thomassen (1978). Fouquet, J.-L.; Jolivet, J. L. (1978), "Hypohamiltonian oriented graphs", Cahiers Centre Études Rech. Opér., 20 (2): 171–181, MR 0498218. Grötschel, M.; Wakabayashi, Y. (1980), "Hypohamiltonian digraphs", Methods of Operations Research, 36: 99–119, Zbl 0436.05038. Grötschel, M.; Wakabayashi, Y. (1984), "Constructions of hypotraceable digraphs", in Cottle, R. W.; Kelmanson, M. L.; Korte, B. (eds.), Mathematical Programming (Proc. International Congress, Rio de Janeiro, 1981), North-Holland. Thomassen, Carsten (1978), "Hypohamiltonian graphs and digraphs", Theory and applications of graphs (Proc. Internat. Conf., Western Mich. Univ., Kalamazoo, Mich., 1976), Lecture Notes in Mathematics, vol. 642, Berlin: Springer-Verlag, pp. 557–571, MR 0499523.

arxiv.org

Jooyandeh et al. (2017), using a computer search and Grinberg's theorem. Earlier small planar hypohamiltonian graphs with 42, 57 and 48 vertices, respectively, were found by Wiener & Araya (2009), Hatzel (1979) and Zamfirescu & Zamfirescu (2007). Jooyandeh, Mohammadreza; McKay, Brendan D.; Östergård, Patric R. J.; Pettersson, Ville H.; Zamfirescu, Carol T. (2017), "Planar Hypohamiltonian Graphs on 40 Vertices", Journal of Graph Theory, 84 (2): 121–133, arXiv:1302.2698, Bibcode:2013arXiv1302.2698J, doi:10.1002/jgt.22015. Wiener, Gábor; Araya, Makoto (2009), The ultimate question, arXiv:0904.3012, Bibcode:2009arXiv0904.3012W. Hatzel, W. (1979), "Ein planarer hypohamiltonscher Graph mit 57 Knoten", Math. Ann., 243 (3): 213–216, doi:10.1007/BF01424541, MR 0548801, S2CID 121794449. Zamfirescu, C. T.; Zamfirescu, T. I. (2007), "A planar hypohamiltonian graph with 48 vertices", Journal of Graph Theory, 55 (4): 338–342, doi:10.1002/jgt.20241.

doi.org

Grötschel (1977); Grötschel (1980); Grötschel & Wakabayashi (1981). Grötschel, M. (1977), "Hypohamiltonian facets of the symmetric travelling salesman polytope", Zeitschrift für Angewandte Mathematik und Mechanik, 58: 469–471. Grötschel, M. (1980), "On the monotone symmetric traveling salesman problem: hypohamiltonian/hypotraceable graphs and facets", Mathematics of Operations Research, 5 (2): 285–292, doi:10.1287/moor.5.2.285, JSTOR 3689157. Grötschel, M.; Wakabayashi, Y. (1981), "On the structure of the monotone asymmetric travelling salesman polytope I: hypohamiltonian facets", Discrete Mathematics, 24: 43–59, doi:10.1016/0012-365X(81)90021-2.
Goemans (1995). Goemans, Michel X. (1995), "Worst-case comparison of valid inequalities for the TSP", Mathematical Programming, 69 (1–3): 335–349, CiteSeerX 10.1.1.52.8008, doi:10.1007/BF01585563, S2CID 214113.
Thomassen (1981). Thomassen, Carsten (1981), "Planar cubic hypo-Hamiltonian and hypotraceable graphs", Journal of Combinatorial Theory, Series B, 30: 36–44, doi:10.1016/0095-8956(81)90089-7, MR 0609592.
The existence of planar hypohamiltonian graphs was posed as an open question by Chvátal (1973), and Chvátal, Klarner & Knuth (1972) offered a $5 prize for the construction of one. Thomassen (1976) used Grinberg's theorem to find planar hypohamiltonian graphs of girth 3, 4, and 5 and showed that there exist infinitely many planar hypohamiltonian graphs. Chvátal, V. (1973), "Flip-flops in hypo-Hamiltonian graphs", Canadian Mathematical Bulletin, 16: 33–41, doi:10.4153/CMB-1973-008-9, MR 0371722. Chvátal, V.; Klarner, D. A.; Knuth, D. E. (1972), Selected Combinatorial Research Problems (PDF), Tech. Report STAN-CS-72-292, Computer Science Department, Stanford University. Thomassen, Carsten (1976), "Planar and infinite hypohamiltonian and hypotraceable graphs", Discrete Mathematics, 14 (4): 377–389, doi:10.1016/0012-365X(76)90071-6, MR 0422086.
Jooyandeh et al. (2017), using a computer search and Grinberg's theorem. Earlier small planar hypohamiltonian graphs with 42, 57 and 48 vertices, respectively, were found by Wiener & Araya (2009), Hatzel (1979) and Zamfirescu & Zamfirescu (2007). Jooyandeh, Mohammadreza; McKay, Brendan D.; Östergård, Patric R. J.; Pettersson, Ville H.; Zamfirescu, Carol T. (2017), "Planar Hypohamiltonian Graphs on 40 Vertices", Journal of Graph Theory, 84 (2): 121–133, arXiv:1302.2698, Bibcode:2013arXiv1302.2698J, doi:10.1002/jgt.22015. Wiener, Gábor; Araya, Makoto (2009), The ultimate question, arXiv:0904.3012, Bibcode:2009arXiv0904.3012W. Hatzel, W. (1979), "Ein planarer hypohamiltonscher Graph mit 57 Knoten", Math. Ann., 243 (3): 213–216, doi:10.1007/BF01424541, MR 0548801, S2CID 121794449. Zamfirescu, C. T.; Zamfirescu, T. I. (2007), "A planar hypohamiltonian graph with 48 vertices", Journal of Graph Theory, 55 (4): 338–342, doi:10.1002/jgt.20241.
Steffen (1998); Steffen (2001). Steffen, E. (1998), "Classification and characterizations of snarks", Discrete Mathematics, 188 (1–3): 183–203, doi:10.1016/S0012-365X(97)00255-0, MR 1630478. Steffen, E. (2001), "On bicritical snarks", Math. Slovaca, 51 (2): 141–150, MR 1841443.
Collier & Schmeichel (1977). Collier, J. B.; Schmeichel, E. F. (1977), "New flip-flop constructions for hypohamiltonian graphs", Discrete Mathematics, 18 (3): 265–271, doi:10.1016/0012-365X(77)90130-3, MR 0543828.
Robertson (1969) proved that these graphs are non-Hamiltonian, while it is straightforward to verify that their one-vertex deletions are Hamiltonian. See Alspach (1983) for a classification of non-Hamiltonian generalized Petersen graphs. Robertson, G. N. (1969), Graphs minimal under girth, valency and connectivity constraints, Ph. D. thesis, Waterloo, Ontario: University of Waterloo. Alspach, B. R. (1983), "The classification of Hamiltonian generalized Petersen graphs", Journal of Combinatorial Theory, Series B, 34 (3): 293–312, doi:10.1016/0095-8956(83)90042-4, MR 0714452.
Thomassen (1974a); Doyen & van Diest (1975). Thomassen, Carsten (1974a), "Hypohamiltonian and hypotraceable graphs", Discrete Mathematics, 9: 91–96, doi:10.1016/0012-365X(74)90074-0, MR 0347682. Doyen, J.; van Diest, V. (1975), "New families of hypohamiltonian graphs", Discrete Mathematics, 13 (3): 225–236, doi:10.1016/0012-365X(75)90020-5, MR 0416979.
Skupień (1989); Skupień (2007). Skupień, Z. (1989), "Exponentially many hypohamiltonian graphs", Graphs, Hypergraphs and Matroids III (Proc. Conf. Kalsk 1988), Zielona Góra: Higher College of Engineering, pp. 123–132. As cited by Skupień (2007). Skupień, Z. (2007), "Exponentially many hypohamiltonian snarks", 6th Czech-Slovak International Symposium on Combinatorics, Graph Theory, Algorithms and Applications, Electronic Notes in Discrete Mathematics, vol. 28, pp. 417–424, doi:10.1016/j.endm.2007.01.059.
Kapoor, Kronk & Lick (1968); Kronk (1969); Grünbaum (1974); Thomassen (1974a). Kapoor, S. F.; Kronk, H. V.; Lick, D. R. (1968), "On detours in graphs", Canadian Mathematical Bulletin, 11 (2): 195–201, doi:10.4153/CMB-1968-022-8, MR 0229543. Kronk, H. V. (1969), Klee, V. (ed.), "Does there exist a hypotraceable graph?", Research Problems, American Mathematical Monthly, 76 (7): 809–810, doi:10.2307/2317879, JSTOR 2317879. Grünbaum, B. (1974), "Vertices missed by longest paths or circuits", Journal of Combinatorial Theory, Series A, 17: 31–38, doi:10.1016/0097-3165(74)90025-9, MR 0349474. Thomassen, Carsten (1974a), "Hypohamiltonian and hypotraceable graphs", Discrete Mathematics, 9: 91–96, doi:10.1016/0012-365X(74)90074-0, MR 0347682.

harvard.edu

ui.adsabs.harvard.edu

Jooyandeh et al. (2017), using a computer search and Grinberg's theorem. Earlier small planar hypohamiltonian graphs with 42, 57 and 48 vertices, respectively, were found by Wiener & Araya (2009), Hatzel (1979) and Zamfirescu & Zamfirescu (2007). Jooyandeh, Mohammadreza; McKay, Brendan D.; Östergård, Patric R. J.; Pettersson, Ville H.; Zamfirescu, Carol T. (2017), "Planar Hypohamiltonian Graphs on 40 Vertices", Journal of Graph Theory, 84 (2): 121–133, arXiv:1302.2698, Bibcode:2013arXiv1302.2698J, doi:10.1002/jgt.22015. Wiener, Gábor; Araya, Makoto (2009), The ultimate question, arXiv:0904.3012, Bibcode:2009arXiv0904.3012W. Hatzel, W. (1979), "Ein planarer hypohamiltonscher Graph mit 57 Knoten", Math. Ann., 243 (3): 213–216, doi:10.1007/BF01424541, MR 0548801, S2CID 121794449. Zamfirescu, C. T.; Zamfirescu, T. I. (2007), "A planar hypohamiltonian graph with 48 vertices", Journal of Graph Theory, 55 (4): 338–342, doi:10.1002/jgt.20241.

jstor.org

Grötschel (1977); Grötschel (1980); Grötschel & Wakabayashi (1981). Grötschel, M. (1977), "Hypohamiltonian facets of the symmetric travelling salesman polytope", Zeitschrift für Angewandte Mathematik und Mechanik, 58: 469–471. Grötschel, M. (1980), "On the monotone symmetric traveling salesman problem: hypohamiltonian/hypotraceable graphs and facets", Mathematics of Operations Research, 5 (2): 285–292, doi:10.1287/moor.5.2.285, JSTOR 3689157. Grötschel, M.; Wakabayashi, Y. (1981), "On the structure of the monotone asymmetric travelling salesman polytope I: hypohamiltonian facets", Discrete Mathematics, 24: 43–59, doi:10.1016/0012-365X(81)90021-2.
Kapoor, Kronk & Lick (1968); Kronk (1969); Grünbaum (1974); Thomassen (1974a). Kapoor, S. F.; Kronk, H. V.; Lick, D. R. (1968), "On detours in graphs", Canadian Mathematical Bulletin, 11 (2): 195–201, doi:10.4153/CMB-1968-022-8, MR 0229543. Kronk, H. V. (1969), Klee, V. (ed.), "Does there exist a hypotraceable graph?", Research Problems, American Mathematical Monthly, 76 (7): 809–810, doi:10.2307/2317879, JSTOR 2317879. Grünbaum, B. (1974), "Vertices missed by longest paths or circuits", Journal of Combinatorial Theory, Series A, 17: 31–38, doi:10.1016/0097-3165(74)90025-9, MR 0349474. Thomassen, Carsten (1974a), "Hypohamiltonian and hypotraceable graphs", Discrete Mathematics, 9: 91–96, doi:10.1016/0012-365X(74)90074-0, MR 0347682.

oeis.org

Aldred, McKay & Wormald (1997). See also (sequence A141150 in the OEIS).

psu.edu

citeseerx.ist.psu.edu

Goemans (1995). Goemans, Michel X. (1995), "Worst-case comparison of valid inequalities for the TSP", Mathematical Programming, 69 (1–3): 335–349, CiteSeerX 10.1.1.52.8008, doi:10.1007/BF01585563, S2CID 214113.

semanticscholar.org

api.semanticscholar.org

Goemans (1995). Goemans, Michel X. (1995), "Worst-case comparison of valid inequalities for the TSP", Mathematical Programming, 69 (1–3): 335–349, CiteSeerX 10.1.1.52.8008, doi:10.1007/BF01585563, S2CID 214113.
Jooyandeh et al. (2017), using a computer search and Grinberg's theorem. Earlier small planar hypohamiltonian graphs with 42, 57 and 48 vertices, respectively, were found by Wiener & Araya (2009), Hatzel (1979) and Zamfirescu & Zamfirescu (2007). Jooyandeh, Mohammadreza; McKay, Brendan D.; Östergård, Patric R. J.; Pettersson, Ville H.; Zamfirescu, Carol T. (2017), "Planar Hypohamiltonian Graphs on 40 Vertices", Journal of Graph Theory, 84 (2): 121–133, arXiv:1302.2698, Bibcode:2013arXiv1302.2698J, doi:10.1002/jgt.22015. Wiener, Gábor; Araya, Makoto (2009), The ultimate question, arXiv:0904.3012, Bibcode:2009arXiv0904.3012W. Hatzel, W. (1979), "Ein planarer hypohamiltonscher Graph mit 57 Knoten", Math. Ann., 243 (3): 213–216, doi:10.1007/BF01424541, MR 0548801, S2CID 121794449. Zamfirescu, C. T.; Zamfirescu, T. I. (2007), "A planar hypohamiltonian graph with 48 vertices", Journal of Graph Theory, 55 (4): 338–342, doi:10.1002/jgt.20241.

stanford.edu

i.stanford.edu

The existence of planar hypohamiltonian graphs was posed as an open question by Chvátal (1973), and Chvátal, Klarner & Knuth (1972) offered a $5 prize for the construction of one. Thomassen (1976) used Grinberg's theorem to find planar hypohamiltonian graphs of girth 3, 4, and 5 and showed that there exist infinitely many planar hypohamiltonian graphs. Chvátal, V. (1973), "Flip-flops in hypo-Hamiltonian graphs", Canadian Mathematical Bulletin, 16: 33–41, doi:10.4153/CMB-1973-008-9, MR 0371722. Chvátal, V.; Klarner, D. A.; Knuth, D. E. (1972), Selected Combinatorial Research Problems (PDF), Tech. Report STAN-CS-72-292, Computer Science Department, Stanford University. Thomassen, Carsten (1976), "Planar and infinite hypohamiltonian and hypotraceable graphs", Discrete Mathematics, 14 (4): 377–389, doi:10.1016/0012-365X(76)90071-6, MR 0422086.

zbmath.org

Fouquet & Jolivet (1978); Grötschel & Wakabayashi (1980); Grötschel & Wakabayashi (1984); Thomassen (1978). Fouquet, J.-L.; Jolivet, J. L. (1978), "Hypohamiltonian oriented graphs", Cahiers Centre Études Rech. Opér., 20 (2): 171–181, MR 0498218. Grötschel, M.; Wakabayashi, Y. (1980), "Hypohamiltonian digraphs", Methods of Operations Research, 36: 99–119, Zbl 0436.05038. Grötschel, M.; Wakabayashi, Y. (1984), "Constructions of hypotraceable digraphs", in Cottle, R. W.; Kelmanson, M. L.; Korte, B. (eds.), Mathematical Programming (Proc. International Congress, Rio de Janeiro, 1981), North-Holland. Thomassen, Carsten (1978), "Hypohamiltonian graphs and digraphs", Theory and applications of graphs (Proc. Internat. Conf., Western Mich. Univ., Kalamazoo, Mich., 1976), Lecture Notes in Mathematics, vol. 642, Berlin: Springer-Verlag, pp. 557–571, MR 0499523.