On H-Linked Graphs |
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Authors: | Michael Ferrara Ronald Gould Gerard Tansey Thor Whalen |
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Institution: | (1) Dept. Math, University of Colorado at Denver, Denver, CO 80217, USA;(2) Dept. Math and CS, Emory University, Atlanta, GA 30322, USA;(3) Dept. Math, Agnes Scott College, Atlanta, GA 30030, USA;(4) Metron Inc. Reston, VA 20190, USA |
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Abstract: | For a fixed multigraph H, possibly containing loops, with V(H)={h1, . . . , hk}, we say a graph G is H-linked if for every choice of k vertices v1, . . . , vk in G, there exists a subdivision of H in G such that vi represents hi (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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