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Article overview
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Constructing Internally Disjoint Pendant Steiner Trees in Cartesian Product Networks | | Yaping Mao
; | | Date: |
28 Aug 2015 | | Abstract: | The concept of pedant tree-connectivity was introduced by Hager in 1985. For
a graph $G=(V,E)$ and a set $Ssubseteq V(G)$ of at least two vertices,
emph{an $S$-Steiner tree} or emph{a Steiner tree connecting $S$} (or simply,
emph{an $S$-tree}) is a such subgraph $T=(V’,E’)$ of $G$ that is a tree with
$Ssubseteq V’$. For an $S$-Steiner tree, if the degree of each vertex in $S$
is equal to one, then this tree is called a emph{pedant $S$-Steiner tree}. Two
pedant $S$-Steiner trees $T$ and $T’$ are said to be emph{internally disjoint}
if $E(T)cap E(T’)=varnothing$ and $V(T)cap V(T’)=S$. For $Ssubseteq V(G)$
and $|S|geq 2$, the emph{local pedant tree-connectivity} $ au_G(S)$ is the
maximum number of internally disjoint pedant $S$-Steiner trees in $G$. For an
integer $k$ with $2leq kleq n$, emph{pedant tree $k$-connectivity} is
defined as $ au_k(G)=min{ au_G(S),|,Ssubseteq V(G),|S|=k}$. In this
paper, we prove that for any two connected graphs $G$ and $H$, $ au_3(GBox
H)geq
min{3lfloorfrac{ au_3(G)}{2}
floor,3lfloorfrac{ au_3(H)}{2}
floor}$.
Moreover, the bound is sharp. | | Source: | arXiv, 1508.7202 | | Services: | Forum | Review | PDF | Favorites | |
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