engleski

All pairs of pentagons in leapfrog fullerenes are nice

A subgraph $H$ of a graph $G$ with a perfect matching is nice if $G - V(H)$ has a perfect matching. It is well known that all fullerene graphs have perfect matchings and that all fullerene graphs contain some small connected graphs as nice subgraphs. In this contribution we consider fullerene graphs arising from smaller fullerenes {;\em via}; the leapfrog transformation and show that in such graphs each pair of (necessarily disjoint) pentagons is nice. That answers in affirmative a question posed in a recent paper on nice pairs of odd cycles in fullerene graphs.

perfect matching ; nice subgraph ; fullerene graph ; leapfrog fullerene

nije evidentirano