Hamiltonicity in multitriangular graphs

• Autorzy: Peter J. Owens , Hansjoachim Walther
• Języki publikacji: EN

Abstrakty

EN

The family of 5-valent polyhedral graphs whose faces are all triangles or 3s-gons, s ≥ 9, is shown to contain non-hamiltonian graphs and to have a shortness exponent smaller than one.

Słowa kluczowe

EN

polyhedral graphs; longest cycles; shortness exponent

Kategorie tematyczne

• 05C45: Eulerian and Hamiltonian graphs
• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1995
• Tom: 15
• Numer: 1
• Strony: 77-88

Daty

wydano

1995

otrzymano

1994-10-19

Twórcy

autor

Peter J. Owens

• University of Surrey Guildford, GU2 5XH, United Kingdom

autor

Hansjoachim Walther

• Technical University Ilmenau, Institite of Mathematies, PF 327, D-98684 Ilmenau, Germany

Bibliografia

• [1] E. J. Grinberg, Planehomogeneous graphs of degree three without Hamiltonian circuits, Latvian Math. Yearbook 4 (1968) 51-58 (in Russian).
• [2] B. Grünbaum and H. Walther, Shortness exponents of families of graphs, J. Combin. Theory (A) 14 (1973) 364-385, doi: 10.1016/0097-3165(73)90012-5.
• [3] J. Harant, Über den Shortness Exponent regulärer Polyedergraphen mit genau zwei Typen von Elementarflächen, Thesis A, Ilmenau Institute of Technology (1982).
• [4] D. A. Holton and B. D. McKay, The smallest non-hamiltonian 3-connected cubic planar graphs have 38 vertices, J. Combin. Theory (B) 45 (1988) 305-319, with correction, J. Combin. Theory (B) 47 (1989) 248.
• [5] P. J. Owens, Non-hamiltonian simple 3-polytopes whose faces are all 5-gons or 7-gons, Discrete Math. 33 (1981) 107-109.
• [6] P. J. Owens, Regular planar graphs with faces of only two types and shortness parameters, J. Graph Theory 8 (1984) 253-275, doi: 10.1002/jgt.3190080207.
• [7] P. J. Owens, Simple 3-polytopal graphs with edges of only two types and shortness coefficients, Discrete Math. 59 (1986) 107-114, doi: 10.1016/0012-365X(86)90074-9.
• [8] P. J. Owens, Shortness exponents, simple polyhedral graphs and large bridges, unpublished.
• [9] M. Tkáč, Shortness coefficients of simple 3-polytopal graphs with edges of only two types, Discrete Math. 103 (1992) 103-110, doi: 10.1016/0012-365X(92)90045-H.
• [10] M. Tkáč, Simple 3-polytopal graphs with edges of only two types and shortness coefficients, Math. Slovaca 42 (1992) 147-152.
• [11] M. Tkáč, On shortness coefficients of simple 3-polytopal graphs with edges of only one type of face besides triangles, Discrete Math. 128 (1994) 407-413, doi: 10.1016/0012-365X(94)90133-3.
• [12] W. T. Tutte, On Hamiltonian circuits, J. London Math. Soc. 21 (1946) 98-101, doi: 10.1112/jlms/s1-21.2.98.
• [13] H. Walther, Über das Problem der Existenz von Hamiltonkreisen in planaren regulären Graphen, Math. Nachr. 39 (1969) 277-296, doi: 10.1002/mana.19690390407.
• [14] H. Walther, Note on the problems of J.Zaks concerning Hamiltonian 3-polytopes, Discrete Math. 33 (1981) 107-109, doi: 10.1016/0012-365X(81)90265-X.
• [15] H. Walther, A non-hamiltonian five-regular multitriangular polyhedral graph (to appear).
• [16] J. Zaks, Non-Hamiltonian non-Grinbergian graphs, Discrete Math. 17 (1977) 317-321, doi: 10.1016/0012-365X(77)90165-0.
• [17] J. Zaks, Non-Hamiltonian simple 3-polytopes having just two types of faces, Discrete Math. 29 (1980) 87-101, doi: 10.1016/0012-365X(90)90289-T.
• [18] J. Zaks, Non-hamiltonian simple planar graphs, in: Annals of Discrete Math. 12 (North - Holland, 1982) 255-263.

Identyfikatory

DOI

10.7151/dmgt.1009