Bounding mean orders of sub-$k$-trees of $k$-trees
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866929304442503168 |
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| author | Cambie, Stijn McCoy, Bradley Wagner, Stephan Yap, Corrine |
| author_facet | Cambie, Stijn McCoy, Bradley Wagner, Stephan Yap, Corrine |
| contents | For a $k$-tree $T$, we prove that the maximum local mean order is attained in a $k$-clique of degree $1$ and that it is not more than twice the global mean order. We also bound the global mean order if $T$ has no $k$-cliques of degree $2$ and prove that for large order, the $k$-star attains the minimum global mean order. These results solve the remaining problems of Stephens and Oellermann [J. Graph Theory 88 (2018), 61-79] concerning the mean order of sub-$k$-trees of $k$-trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_16545 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bounding mean orders of sub-$k$-trees of $k$-trees Cambie, Stijn McCoy, Bradley Wagner, Stephan Yap, Corrine Combinatorics 05C05, 05C35 For a $k$-tree $T$, we prove that the maximum local mean order is attained in a $k$-clique of degree $1$ and that it is not more than twice the global mean order. We also bound the global mean order if $T$ has no $k$-cliques of degree $2$ and prove that for large order, the $k$-star attains the minimum global mean order. These results solve the remaining problems of Stephens and Oellermann [J. Graph Theory 88 (2018), 61-79] concerning the mean order of sub-$k$-trees of $k$-trees. |
| title | Bounding mean orders of sub-$k$-trees of $k$-trees |
| topic | Combinatorics 05C05, 05C35 |
| url | https://arxiv.org/abs/2309.16545 |