Plane Triangulations Without a Spanning Halin Subgraph II
نویسندگان
چکیده
A Halin graph is a plane graph constructed from a planar drawing of a tree by connecting all leaves of the tree with a cycle which passes around the boundary of the graph. The tree must have four or more vertices and no vertices of degree two. Halin graphs have many nice properties such as being Hamiltonian and remain Hamiltonian after any single vertex deletion. In 1975, Lovász and Plummer conjectured that every 4-connected plane triangulation contains a spanning Halin subgraph. We recently gave a negative answer to this conjecture. In this paper, we construct an infinite class of 5-connected plane triangulations without a spanning Halin subgraph. Our smallest example contains 512 vertices.
منابع مشابه
Plane Triangulations Without a Spanning Halin Subgraph: Counterexamples to the Lovász-Plummer Conjecture on Halin Graphs
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.
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عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 31 شماره
صفحات -
تاریخ انتشار 2017