 More precisely, for any ordering of the graphs in formula_2 into a sequence formula_6, with formula_7 defined to be the length of the longest cycle in graph formula_8, the shortness exponent is defined as
This number is always in the interval from 0 to 1; it is 1 for families of graphs that always contain a Hamiltonian or near-Hamiltonian cycle, and 0 for families of graphs in which the longest cycle length can be smaller than any constant power of the number of vertices.The shortness exponent of the polyhedral graphs is formula_10.A construction based on kleetopes shows that some polyhedral graphs have longest cycle length formula_11, while it has also been proven that every polyhedral graph contains a cycle of length formula_12.