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Article
Graph Linkedness With Prescribed Lengths
International Journal of Graph Theory and its Applications
  • Vincent E. Coll, Jr., Lehigh University
  • Alexander Halperin, Lehigh University
  • Colton Magnant, Georgia Southern University
Document Type
Article
Publication Date
6-1-2016
Disciplines
Abstract

Given a multigraph H, a graph G is H-linked if every injective map f : V (H) -> V (G) can be extended to an H-subdivision (f,g) in G for some g. Given a multigraph H and an integer sequence w = {we | e 2 E(H), we 2}, a graph G is (H, w, m)-linked if every injective map f : V (H) -> V (G) can be extended to an H-subdivision (f,g) in G such that each path g(e) has length we ,..., or we + m. If m = 0, then we say G is (H, w)-linked. We show that the sharp minimum degree condition for a graph to be H-linked is the same as the sharp minimum degree condition for a large graph to be (H, w, m)-linked for m 1 and all sets w with each value we 2 w at least 14. Additionally, we establish a sharp minimum degree condition for a large graph to be (H, w)-linked.

Citation Information
Vincent E. Coll, Alexander Halperin and Colton Magnant. "Graph Linkedness With Prescribed Lengths" International Journal of Graph Theory and its Applications Vol. 2 Iss. 1 (2016) p. 1 - 21
Available at: http://works.bepress.com/colton_magnant/69/