Connectivity for Kite-Linked Graphs

Abstract

For a given graph H, a graph G is H-linked if, for every injection ϕ : V (H) → V (G), the graph G contains a subdivision of H with ϕ(v) corresponding to v, for each v ∈ V (H). Let f (H) be the minimum integer k such that every k-connected graph is H-linked. Among graphs H with at least four vertices, the exact value f (H) is only know when H is a path with four vertices or a cycle with four vertices. A kite is graph obtained from K4 by deleting two adjacent edges, i.e., a triangle together with a pendant edge.Recently, Liu, Rolek and Yu proved that every 8-connected graph is kite-linked. The exact value of f (H) when H is the kite remains open. In this paper, we settle this problem by showing that every 7-connected graph is kite-linked.