Schrijver Graphs and Projective Quadrangulations

  • Tomáš Kaiser
  • Matěj Stehlík


In a recent paper, Kaiser and Stehlík (J Combin Theory Ser B 113:1–17, 2015) have extended the concept of quadrangulation of a surface to higher dimension, and showed that every quadrangulation of the n-dimensional projective space \(\mathbb{P}^{n}\) is at least (n + 2)-chromatic, unless it is bipartite. They conjectured that for any integers k ≥ 1 and n ≥ 2k + 1, the Schrijver graph SG(n, k) contains a spanning subgraph which is a non-bipartite quadrangulation of \(\mathbb{P}^{n-2k}\). The purpose of this paper is to prove the conjecture.



We thank two anonymous reviewers for a careful reading of the first versions and a number of suggestions. This project was started while the second author was visiting Fabricio Benevides and Víctor Campos at the Universidade Federal do Ceará.


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© Springer International publishing AG 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Institute for Theoretical Computer Science (CE-ITI), and European Centre of Excellence NTIS (New Technologies for the Information Society)University of West BohemiaPilsenCzech Republic
  2. 2.Laboratoire G-SCOPUniversité Grenoble AlpesGrenobleFrance

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