Geodesic
Bounding mean orders of sub-\(k\)-trees of \(k\)-trees
Stijn Cambie ; Bradley McCoy ; Stephan Wagner1 ; Corrine Yap
1Uppsala University
The electronic journal of combinatorics, Tome 31 (2024) no. 1
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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.
DOI : 10.37236/12426
Classification : 05C05, 05C35
Mots-clés : maximum local mean order, global mean order

Stijn Cambie    ; Bradley McCoy     ; Stephan Wagner  1   ; Corrine Yap 

1 Uppsala University 
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     title = {Bounding mean orders of sub-\(k\)-trees of \(k\)-trees},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {1},
     doi = {10.37236/12426},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/12426/}
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Stijn Cambie; Bradley McCoy ; Stephan Wagner; Corrine Yap. Bounding mean orders of sub-\(k\)-trees of \(k\)-trees. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/12426

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