Abstract
It is shown that every fullerene graph G is cyclically 5-edge-connected, i.e., that G cannot be separated into two components, each containing a cycle, by deletion of fewer than five edges. The result is then generalized to the case of (k,6)-cages, i.e., polyhedral cubic graphs whose faces are only k-gons and hexagons. Certain linear and exponential lower bounds on the number of perfect matchings in such graphs are also established.
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Došlić, T. Cyclical Edge-Connectivity of Fullerene Graphs and (k, 6)-Cages. Journal of Mathematical Chemistry 33, 103–112 (2003). https://doi.org/10.1023/A:1023299815308
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DOI: https://doi.org/10.1023/A:1023299815308