关于k -树的k -树的局部和全局平均阶

IF 0.7 4区数学 Q2 MATHEMATICS

Electronic Journal of Combinatorics Pub Date : 2023-03-10 DOI:10.37236/11280

Zuwen Luo, Kexiang Xu

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引用次数: 2

摘要

本文证明了对于给定的$k$-树$T$和$k$-团$C$，包含$C$的$T$的所有子$k$-树的局部平均阶不小于$T$的所有子$k$-树的全局平均阶，并且路径型$k$-树在给定阶的所有$k$-树中具有最小的全局平均子$k$-树阶。这两个结果给出了Stephens和Oellermann的两个问题的解[J]。图论88(2018)，61-79]关于$k$-树的$k$-树的平均阶。此外，作为$k$树上的函数的平均子$k$树阶被证明是关于包含的单调的。这推广了Jamison在$k=1$ [J]情况下的结果。Combin。Ser的理论。B 35(1983)， 207-223]。

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On the Local and Global Mean Orders of Sub-$k$-Trees of $k$-Trees

In this paper we show that for a given $k$-tree $T$ with a $k$-clique $C$, the local mean order of all sub-$k$-trees of $T$ containing $C$ is not less than the global mean order of all sub-$k$-trees of $T$, and the path-type $k$-trees have the smallest global mean sub-$k$-tree order among all $k$-trees of a given order. These two results give solutions to two problems of Stephens and Oellermann [J. Graph Theory 88 (2018), 61-79] concerning the mean order of sub-$k$-trees of $k$-trees. Furthermore, the mean sub-$k$-tree order as a function on $k$-trees is shown to be monotone with respect to inclusion. This generalizes Jamison's result for the case $k=1$ [J. Combin. Theory Ser. B 35 (1983), 207-223].

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来源期刊

Electronic Journal of Combinatorics 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

212

审稿时长

3-6 weeks

期刊介绍： The Electronic Journal of Combinatorics (E-JC) is a fully-refereed electronic journal with very high standards, publishing papers of substantial content and interest in all branches of discrete mathematics, including combinatorics, graph theory, and algorithms for combinatorial problems.