Xiying Du, Characterizing (2,3)-linked graphs
We say a graph $G$ is $(2,m)$-linked if, for every choice of $m+2$ distinct vertices $a_1,\ldots,a_m,b_1,b_2$ in $G$, there exist two vertex-disjoint connected subgraphs $A$ and $B$ of $G$ such that $\{a_1,\ldots,a_m\}\subseteq V(A)$ and $\{b_1,b_2\}\subseteq V(B)$. A related notion is $k$-linkedness: a graph is $k$-linked if, for any distinct vertices $s_1,\ldots,s_k,t_1,\ldots,t_k$, it contains $k$ pairwise …