Local Conditions for Exponentially Many Subdivisions

  title={Local Conditions for Exponentially Many Subdivisions},
  author={Hong Liu and Maryam Sharifzadeh and Katherine Staden},
  journal={Combinatorics, Probability & Computing},
Given a graph F , let st(F ) be the number of subdivisions of F , each with a different vertex set, which one can guarantee in a graph G in which every edge lies in at least t copies of F . In 1990, Tuza asked for which graphs F and large t, one has that st(F ) is exponential in a power of t. We show that, somewhat surprisingly, the only such F are complete… CONTINUE READING