至少有一半的蛙跳富勒烯图具有指数数量的Hamilton圈
At least half of the leapfrog fullerene graphs have exponentially many Hamilton cycles
摘要：
富勒烯图是具有五边形和六边形面的3连通立方可平面图。可平面图的蛙跳变换产生给定图的对偶图的结构。如果一个富勒烯图可以通过蛙跳变换从另一个富勒烯图得到，则称该图为蛙跳图。证明了$n=12k-6$顶点上的蛙跳富勒烯图至少有$2^{k}$ Hamilton圈.
英文摘要：
A fullerene graph is a 3-connected cubic planar graph with pentagonal and hexagonal faces. The leapfrog transformation of a planar graph produces the trucation of the dual of the given graph. A fullerene graph is leapfrog if it can be obtained from another fullerene graph by the leapfrog transformation. We prove that leapfrog fullerene graphs on $n=12k-6$ vertices have at least $2^{k}$ Hamilton cycles.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
