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Planar and infinite hypohamiltonian and hypotraceable graphs. (English) Zbl 0322.05130


MSC:

05C35 Extremal problems in graph theory
05C10 Planar graphs; geometric and topological aspects of graph theory
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References:

[1] Chvátal, V., Flip-flops in hypohamiltonian graphs, Can. Math. Bull., 16, 33-41 (1973) · Zbl 0253.05142
[2] Chvátal, V., New directions in hamiltonian graph theory, (Harary, F., New Directions in Graph Theory (1973), Academic Press: Academic Press New York) · Zbl 0271.05120
[3] Chvátal, V.; Klarner, D. A.; Knuth, D. E., Selected combinatorial research problems (1972), Stanford University: Stanford University Stanford, Problem 19.
[4] Doyen, J.; Van Diest, V., New families of hypohamiltonian graphs, Discrete Math., 13, 225-236 (1975) · Zbl 0312.05114
[5] Faulkner, G. B.; Younger, D. H., Non-hamiltonian cubic planar maps, Discrete Math., 7, 67-74 (1974) · Zbl 0271.05106
[6] Grinberg, E., Plane homogeneous graphs of degree three without Hamiltonian circuits, Latvian Math. Yearbook, Izdal. “Zinatne”, 4, 51-58 (1968), (in Russian) · Zbl 0185.27901
[7] Grünbaum, B., Polytopes, graphs and complexes, Bull. Am. Math. Soc., 76, 1131-1201 (1970) · Zbl 0211.25001
[8] Grünbaum, B., Vertices missed by longest paths or circuits, J. Combin. Theory, 17, 31-38 (1974) · Zbl 0259.05120
[9] Guy, R., Monthly research problems, 1969-1973, Am. Math. Monthly, 80, 1120-1128 (1973)
[10] Harary, F., Graph Theory (1969), Addison-Wesley: Addison-Wesley Reading, Mass · Zbl 0797.05064
[11] Herz, J. C.; Duby, J. J.; Vigué, F., Recherche systématique des graphes hypohamiltonian, (Rosenstiehl, P., Theorie des Graphes (1967), Dunod: Dunod Paris), 153-160 · Zbl 0196.56102
[12] Honsberger, R., Mathematical Gems (1973), Math. Assoc. of America, Chapter 7 · Zbl 0281.00004
[13] Thomassen, C., Hypohamiltonian and hypotraceable graphs, Discrete Math., 9, 91-96 (1974) · Zbl 0278.05110
[14] Thomassen, C., On hypohamiltonian graphs, Discrete Math., 10, 383-390 (1974) · Zbl 0286.05122
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