All Pairs of Pentagons in Leapfrog Fullerenes Are Nice

A subgraph H of a graph G with perfect matching is nice if G−V(H) has 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 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.

Reflections on the Construction of the New Urbanization in Shanxi

IntroductiNew urbanization is an important principle of promoting urbanization in our country. It’s also a major opportunity to achieve leapfrog-transformation development for Shanxi Province. According to China's new urbanization concept, explained the significance of the new urbanization construction in Shanxi Province. According to relevant statistics and related data analyses the current situation and the current problems of urbanization construction in Shanxi Province thus made recommendations of the urbanization construction of Shanxi Province accordingly.