Abstract
For a fixed multigraph H, possibly containing loops, with V(H)={h1, . . . , h k }, we say a graph G is H-linked if for every choice of k vertices v1, . . . , v k in G, there exists a subdivision of H in G such that v i represents h i (for all i). This notion clearly generalizes the concept of k-linked graphs (as well as other properties). In this paper we determine, for a connected multigraph H and for any sufficiently large graph G, a sharp lower bound on δ(G) (depending upon H) such that G is H-linked.
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Ferrara, M., Gould, R., Tansey, G. et al. On H-Linked Graphs. Graphs and Combinatorics 22, 217–224 (2006). https://doi.org/10.1007/s00373-006-0651-6
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DOI: https://doi.org/10.1007/s00373-006-0651-6