On the number of minimum dominating sets and total dominating sets in forests

IF 0.9 3区 数学 Q2 MATHEMATICS Journal of Graph Theory Pub Date : 2024-04-29 DOI:10.1002/jgt.23107
Jan Petr, Julien Portier, Leo Versteegen
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Abstract

We show that the maximum number of minimum dominating sets of a forest with domination number γ is at most 5 γ and construct for each γ a tree with domination number γ that has more than 2 5 5 γ minimum dominating sets. Furthermore, we disprove a conjecture about the number of minimum total dominating sets in forests by Henning, Mohr and Rautenbach.

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论森林中最小支配集和总支配集的数量
我们证明了具有支配数的森林的最小支配集的最大数量,并为每一棵具有支配数的树构造了多于最小支配集的最小支配集。此外,我们还推翻了亨宁、莫尔和劳滕巴赫关于森林中最小支配集总数的猜想。
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来源期刊
Journal of Graph Theory
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 .
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