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arXiv · 2309.11885

On the maximum local mean order of sub-k-trees of a k-tree

Zhuo Li·Tianlong Ma·Fengming Dong·Xian'an Jin
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Abstract

For a k-tree T, a generalization of a tree, the local mean order of sub-k-trees of T is the average order of sub-k-trees of T containing a given k-clique. The problem whether the largest local mean order of a tree (i.e., a 1-tree) at a vertex always takes on at a leaf was asked by Jamison in 1984 and was answered by Wagner and Wang in 2016. In 2018, Stephens and Oellermann asked a similar problem: for any k-tree T, does the maximum local mean order of sub-k-trees containing a given k-clique occur at a k-clique that is not a major k-clique of T? In this paper, we give it an affirmative answer.

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Zhuo Li, Tianlong Ma, Fengming Dong, Xian'an Jin. 2023-09-21. On the maximum local mean order of sub-k-trees of a k-tree. https://arxiv.org/abs/2309.11885

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