Independent Domination Number of Planar Triangulations

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2025-07-17 DOI:10.1002/jgt.23285

P. Francis, Abraham M. Illickan, Lijo M. Jose, Deepak Rajendraprasad

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引用次数: 0

Abstract

We show that every planar triangulation on $n$ vertices has a maximal independent set of size at most $n / 3$ . This affirms a conjecture by Botler, Fernandes, and Gutiérrez (Electron. J. Comb., 2024) based on an open question of Goddard and Henning (Appl. Math. Comput., 2020). Since a maximal independent set is a special type of dominating set (independent dominating set), this is a structural strengthening of a major result by Matheson and Tarjan (Eur. J. Comb., 1996) that every triangulated disc has a dominating set of size at most $n / 3$ , but restricted to triangulations.

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平面三角剖分的独立支配数

我们证明了在n个顶点上的每个平面三角剖分都有一个最大独立集，其大小最多为n / 3。这证实了Botler、Fernandes和gutisamurez （Electron）的一个猜想。j .梳子。， 2024)基于戈达德和亨宁（苹果公司）的一个开放问题。数学。第一版。, 2020)。由于极大独立集是一种特殊类型的支配集（独立支配集），这是Matheson和Tarjan （Eur）的一个主要结果的结构强化。j .梳子。（1996），每个三角化圆盘都有一个最大为n / 3的支配集，但仅限于三角化。

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .