Steiner convex sets of grids

Tanja Gologranc
Faculty of Natural Sciences and Mathematics, University of Maribor


Minisymposium: GRAPH PRODUCTS

Content: The Steiner tree of a (multi)set of vertices $R =\{u_1,\ldots ,u_k\} \subseteq V(G)$ is the smallest tree in $G$ that contains all vertices of $R$. The Steiner distance $d(R)$ of a set $R$ is the number of edges in a Steiner tree $T$ for $R$. The $k$-Steiner interval of a set $R \subseteq V(G)$, $I(R),$ consists of all vertices in $G$ that lie on some Steiner tree for $R$. A set $S$ of vertices is $k$-Steiner convex, if the Steiner interval $I(R)$ of every (multi)set $R$ on $k$ vertices is contained in $S$. We say that a set $S$ is Steiner convex if it is $k$-Steiner convex, for every $k \geq 2.$ In this talk the characterization of Steiner convex sets of grids will be presented.

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