# Hamiltonicity in multitriangular graphs

Peter J. Owens; Hansjoachim Walther

Discussiones Mathematicae Graph Theory (1995)

- Volume: 15, Issue: 1, page 77-88
- ISSN: 2083-5892

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topPeter J. Owens, and Hansjoachim Walther. "Hamiltonicity in multitriangular graphs." Discussiones Mathematicae Graph Theory 15.1 (1995): 77-88. <http://eudml.org/doc/270460>.

@article{PeterJ1995,

abstract = {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.},

author = {Peter J. Owens, Hansjoachim Walther},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {polyhedral graphs; longest cycles; shortness exponent; hamiltonicity; multitriangular graphs; longest cycle; faces; triangles; Tutte subgraphs},

language = {eng},

number = {1},

pages = {77-88},

title = {Hamiltonicity in multitriangular graphs},

url = {http://eudml.org/doc/270460},

volume = {15},

year = {1995},

}

TY - JOUR

AU - Peter J. Owens

AU - Hansjoachim Walther

TI - Hamiltonicity in multitriangular graphs

JO - Discussiones Mathematicae Graph Theory

PY - 1995

VL - 15

IS - 1

SP - 77

EP - 88

AB - 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.

LA - eng

KW - polyhedral graphs; longest cycles; shortness exponent; hamiltonicity; multitriangular graphs; longest cycle; faces; triangles; Tutte subgraphs

UR - http://eudml.org/doc/270460

ER -

## References

top- [1] E. J. Grinberg, Planehomogeneous graphs of degree three without Hamiltonian circuits, Latvian Math. Yearbook 4 (1968) 51-58 (in Russian). Zbl0185.27901
- [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. Zbl0263.05103
- [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. Zbl0607.05051
- [5] P. J. Owens, Non-hamiltonian simple 3-polytopes whose faces are all 5-gons or 7-gons, Discrete Math. 33 (1981) 107-109. Zbl0473.05043
- [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. Zbl0541.05037
- [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. Zbl0586.05027
- [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. Zbl0776.05093
- [10] M. Tkáč, Simple 3-polytopal graphs with edges of only two types and shortness coefficients, Math. Slovaca 42 (1992) 147-152. Zbl0768.05065
- [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. Zbl0798.05018
- [12] W. T. Tutte, On Hamiltonian circuits, J. London Math. Soc. 21 (1946) 98-101, doi: 10.1112/jlms/s1-21.2.98. Zbl0061.41306
- [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. Zbl0169.26401
- [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). Zbl0854.05065
- [16] J. Zaks, Non-Hamiltonian non-Grinbergian graphs, Discrete Math. 17 (1977) 317-321, doi: 10.1016/0012-365X(77)90165-0. Zbl0357.05052
- [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. Zbl0445.05065
- [18] J. Zaks, Non-hamiltonian simple planar graphs, in: Annals of Discrete Math. 12 (North - Holland, 1982) 255-263. Zbl0493.05022

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