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Your search keyword '"05C10, 05C69"' showing total 2 results
Start Over Descriptor "05C10, 05C69" Publisher elsevier bv
2 results on '"05C10, 05C69"'

1. The domination number of plane triangulations

Author

Simon Špacapan

Subjects
Triangulation (topology), Class (set theory), Plane (geometry), Domination analysis, 010102 general mathematics, 0102 computer and information sciences, Computer Science::Computational Geometry, 01 natural sciences, Theoretical Computer Science, Combinatorics, Computational Theory and Mathematics, 010201 computation theory & mathematics, Dominating set, 05C10, 05C69, FOS: Mathematics, Mathematics - Combinatorics, Discrete Mathematics and Combinatorics, Combinatorics (math.CO), 0101 mathematics, Graph operations, Mathematics
Abstract

We introduce a class of plane graphs called weak near-triangulations, and prove that this class is closed under certain graph operations. Then we use the properties of weak near-triangulations to prove that every plane triangulation on n > 6 vertices has a dominating set of size at most 17 n / 53 . This improves the bound n / 3 obtained by Matheson and Tarjan.

Published
2020

2. Dominating sets in plane triangulations

Author

Michael J. Pelsmajer and Erika L. C. King

Subjects
Discrete mathematics, Vertex (graph theory), Computer Science::Computational Geometry, Triangulation, Theoretical Computer Science, Combinatorics, In plane, Dominating set, Computer Science::Discrete Mathematics, 05C10, 05C69, FOS: Mathematics, Mathematics - Combinatorics, Discrete Mathematics and Combinatorics, Combinatorics (math.CO), Point set triangulation, Mathematics
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., 14 pages, 6 figures; Revised lemmas 6-8, clarified arguments and fixed typos, result unchanged

Published
2010

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