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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
##### Keywords:
light graph; plane graphs
Full Text:
##### References:
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