Dominating Sets in Plane Triangulations
Erika L.C. King, Michael J. Pelsmajer
TL;DR
This paper proves that in large plane triangulations with maximum degree 6, the minimum dominating set size is at most one-quarter of the total vertices, confirming a longstanding conjecture for this class.
Contribution
It establishes the conjecture for graphs with maximum degree 6, advancing understanding of dominating sets in plane triangulations.
Findings
Dominating set size at most n/4 for degree 6 triangulations
Confirms Matheson and Tarjan's conjecture for a specific graph class
Provides new bounds for dominating sets in plane graphs
Abstract
In 1996, Matheson and Tarjan conjectured that any n-vertex triangulation with n sufficiently large has a dominating set of size at most n/4. We prove this for graphs of maximum degree 6.
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Taxonomy
TopicsAdvanced Graph Theory Research · Limits and Structures in Graph Theory · Complexity and Algorithms in Graphs