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On the maximum local mean order of sub-k-trees of a k-tree
Citation
Li, Z., Ma, T., Dong, F., & Jin, X. (2024). On the maximum local mean order of sub-k-trees of a k-tree. Journal of Graph Theory, 107(2), 393–409. https://doi.org/10.1002/jgt.23128
Abstract
For a κ-tree T, a generalization of a tree, the local mean order of sub-κ-trees of T is the average order of sub-κ-trees of T containing a given κ-clique. The problem whether the maximum local mean order of a tree (i.e., a 1-tree) at a vertex is always taken on at a leaf was asked by Jamison in 1984 and was answered by Wagner and Wang in 2016. Actually, they proved that the maximum local mean order of a tree at a vertex occurs either at a leaf or at a vertex of degree 2. In 2018, Stephens and Oellermann asked a similar problem: for any κ-tree T, does the maximum local mean order of sub-κ-trees containing a given κ-clique occur at a κ-clique that is not a major κ-clique of T? In this paper, we give it an affirmative answer.
Date Issued
2024
Publisher
Wiley
Journal
Journal of Graph Theory
Project
RP 2/22 DFM
Funding Agency
Ministry of Education, Singapore