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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
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