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On large light graphs in families of polyhedral graphs. (English) Zbl 1216.05123
Summary: A graph \(H\) is said to be light in a family \(\mathcal H\) of graphs if each graph \(G \in \mathcal H\) containing a subgraph isomorphic to \(H\) contains also an isomorphic copy of \(H\) such that each its vertex has the degree (in \(G\)) bounded above by a finite number \(\varphi (H, \mathcal H)\) depending only on \(H\) and \(\mathcal H\). We prove that in the family of all 3-connected plane graphs of minimum degree 5 (or minimum face size 5, respectively), the paths with certain small graphs attached to one of its ends are light.

MSC:
05C75 Structural characterization of families of graphs
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