Abstract
A Halin graph is constructed from a plane embedding of a tree with no vertices of degree 2 by adding a cycle through its leaves in the natural order determined by the embedding. Halin graphs satisfy interesting properties. However, to our knowledge, there are no results giving a positive answer for “spanning Halin subgraph problem” (i.e., which graph has a Halin graph as a spanning subgraph) except for a conjecture by Lovasz and Plummer which states that every 4-connected plane triangulation contains a spanning Halin subgraph. In this paper, we investigate the characterization of forbidden pairs guaranteeing the existence of a spanning Halin subgraph. In particular, we show that the set of such pairs is a very small class. Also, we show that $$\{ K_{1,3}, P_5 \}$$ belongs to the set, but neither $$\{ K_{1,4}, P_5 \}$$ nor $$\{ K_{1,3}, P_6 \}$$ belongs to the set.
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