RT journal article
T1 A Steiner general position problem in graph theory
A1 Klavžar, Sandi
A1 Kuziak, Dorota
A1 Peterin, Iztok
A1 González Yero, Ismael
A2 Estadística e Investigación Operativa
A2 Matemáticas
K1 Steiner distance
K1 Steiner general position set
K1 Steiner general position number
K1 join of graphs
K1 lexicographic product of graphs
AB Let $G$ be a graph. The Steiner distance of $W\subseteq V(G)$ is the minimum size of a connected subgraph of $G$ containing $W$. Such a subgraph is necessarily a tree called a Steiner $W$-tree. The set $A\subseteq V(G)$ is a $k$-Steiner general position set if $V(T_B)\cap A = B$ holds for every set $B\subseteq A$ of cardinality $k$, and for every Steiner $B$-tree $T_B$. The $k$-Steiner general position number $\sgp_k(G)$ of $G$ is the cardinality of a largest $k$-Steiner general position set in $G$. Steiner cliques are introduced and used to bound $\sgp_k(G)$ from below. The $k$-Steiner general position number is determined for trees, cycles and joins of graphs. Lower bounds are presented for split graphs, infinite grids and  lexicographic products. The lower bound for the latter product leads to an exact formula for the general position number of an arbitrary lexicographic product.
PB Springer
SN 1807-0302
YR 2021
FD 2021-08-23
LK http://hdl.handle.net/10498/30895
UL http://hdl.handle.net/10498/30895
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026