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Lightness, heaviness and gravity. (English) Zbl 1111.05027
Summary: The gravity $$g(H,\mathcal H)$$ of a graph $$H$$ in the family of graphs $$\mathcal H$$ is the greatest integer $$n$$ with the property that for every integer $$m$$, there exists a supergraph $$G\in \mathcal H$$ of $$H$$ such that each subgraph of $$G$$ which is isomorphic to $$H$$ contains at least $$n$$ vertices of degree $$\geqslant m$$ in $$G$$. We study the basic properties of the gravity function for various families of plane graphs. We also introduce and study the almost-light graphs and the absolutely heavy graphs. The paper concludes with few open problems.

##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory 05C38 Paths and cycles
##### Keywords:
gravity; light graph; heavy graph; plane graphs
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##### References:
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