@article{795,
  abstract     = {We introduce a common generalization of the strong Hanani–Tutte theorem and the weak Hanani–Tutte theorem: if a graph G has a drawing D in the plane where every pair of independent edges crosses an even number of times, then G has a planar drawing preserving the rotation of each vertex whose incident edges cross each other evenly in D. The theorem is implicit in the proof of the strong Hanani–Tutte theorem by Pelsmajer, Schaefer and Štefankovič. We give a new, somewhat simpler proof.},
  author       = {Fulek, Radoslav and Kynčl, Jan and Pálvölgyi, Dömötör},
  issn         = {1077-8926},
  journal      = {Electronic Journal of Combinatorics},
  number       = {3},
  publisher    = {International Press},
  title        = {{Unified Hanani Tutte theorem}},
  doi          = {10.37236/6663},
  volume       = {24},
  year         = {2017},
}

@article{701,
  abstract     = {A d-dimensional simplex S is called a k-reptile (or a k-reptile simplex) if it can be tiled by k simplices with disjoint interiors that are all mutually congruent and similar to S. For d = 2, triangular k-reptiles exist for all k of the form a^2, 3a^2 or a^2+b^2 and they have been completely characterized by Snover, Waiveris, and Williams. On the other hand, the only k-reptile simplices that are known for d ≥ 3, have k = m^d, where m is a positive integer. We substantially simplify the proof by Matoušek and the second author that for d = 3, k-reptile tetrahedra can exist only for k = m^3. We then prove a weaker analogue of this result for d = 4 by showing that four-dimensional k-reptile simplices can exist only for k = m^2.},
  author       = {Kynčl, Jan and Patakova, Zuzana},
  issn         = {1077-8926},
  journal      = {The Electronic Journal of Combinatorics},
  number       = {3},
  pages        = {1--44},
  publisher    = {International Press},
  title        = {{On the nonexistence of k reptile simplices in ℝ^3 and ℝ^4}},
  volume       = {24},
  year         = {2017},
}