Plane Triangulations Without a Spanning Halin Subgraph: Counterexamples to the Lovász-Plummer Conjecture on Halin Graphs
نویسندگان
چکیده
A Halin graph is a simple plane graph consisting of a tree without degree 2 vertices and a cycle induced by the leaves of the tree. In 1975, Lovász and Plummer conjectured that every 4-connected plane triangulation has a spanning Halin subgraph. In this paper, we construct an infinite family of counterexamples to the conjecture.
منابع مشابه
Lovász-Plummer conjecture on Halin graphs
A Halin graph, defined by Halin [3], is a plane graph H = T ∪ C such that T is a spanning tree of H with no vertices of degree 2 where |T | ≥ 4 and C is a cycle whose vertex set is the set of leaves of T . In his work, as an example of a class of edge-minimal 3-connected plane graphs, Halin constructed this family of plane graphs, which have many interesting properties. Lovász and Plummer [5] n...
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 29 شماره
صفحات -
تاریخ انتشار 2015