Shortness parameters for planar graphs with faces of only one type
Peter J. Owens · Journal of Graph Theory · 1985
Abstract We construct infinite sequences of non‐Hamiltonian graphs and use them to show that the shortness exponent (or, in some cases, the shortness coefficient) is less than one for many classes of 3‐connected planar graphs whose faces are all r‐gons and whose vertices are all p‐valent or q‐valent, where p < q. Three of the five possible values of (r, p) are considered, namely (4.3). (3,3), and (3,4), in conjunction with most of the possible corresponding values of q.