Abstract
A sequence of polyhedral graphsG n is constructed, having only 3-valent and 8-valent vertices and having only 3-gons and 8-gons as faces with the property that the shortness exponent of the sequence as well as the shortness exponent of the sequence of duals is smaller than one.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Ewald,Shortness exponents of families of graphs, Israel J. Math.16 (1973), 53–61.
B. Grünbaum and H. Walther,Shortness exponents of families of graphs, J. Comb. Theory (A)14 (1973), 364–385.
B. Grünbaum and T.S. Motzkin,Longest simple paths in polyhedral graphs, J. London Math. Soc.37 (1962), 152–160.
J. Harant,Über den Shortness Exponent regulärer Polyedergraphen mit genau zwei Typen von Elementarflächen, Thesis A, Ilmenau, Institute of Technology.
P.J. Owens,Regular planar graphs with faces of only two types and shortness parameters, J. Graph Theory8 (1984), 253–275.
M. Tkáč,Note on shortness coefficients of simple 3-polytopal graphs with only one type of faces besides triangles., Discr. Math. (to appear).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Walther, H. Longest cycles in polyhedral graphs. Israel J. Math. 83, 203–212 (1993). https://doi.org/10.1007/BF02764642
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02764642