---
res:
  bibo_abstract:
  - "Van der Holst and Pendavingh introduced a graph parameter σ, which coincides
    with the more famous Colin de Verdière graph parameter μ for small values. However,
    the definition of a is much more geometric/topological directly reflecting embeddability
    properties of the graph. They proved μ(G) ≤ σ(G) + 2 and conjectured σ(G) ≤ σ(G)
    for any graph G. We confirm this conjecture. As far as we know, this is the first
    topological upper bound on σ(G) which is, in general, tight.\r\nEquality between
    μ and σ does not hold in general as van der Holst and Pendavingh showed that there
    is a graph G with μ(G) ≤ 18 and σ(G) ≥ 20. We show that the gap appears at much
    smaller values, namely, we exhibit a graph H for which μ(H) ≥ 7 and σ(H) ≥ 8.
    We also prove that, in general, the gap can be large: The incidence graphs Hq
    of finite projective planes of order q satisfy μ(Hq) ∈ O(q3/2) and σ(Hq) ≥ q2.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Vojtech
      foaf_name: Kaluza, Vojtech
      foaf_surname: Kaluza
      foaf_workInfoHomepage: http://www.librecat.org/personId=21AE5134-9EAC-11EA-BEA2-D7BD3DDC885E
    orcid: 0000-0002-2512-8698
  - foaf_Person:
      foaf_givenName: Martin
      foaf_name: Tancer, Martin
      foaf_surname: Tancer
      foaf_workInfoHomepage: http://www.librecat.org/personId=38AC689C-F248-11E8-B48F-1D18A9856A87
    orcid: 0000-0002-1191-6714
  bibo_doi: 10.1007/s00493-021-4443-7
  bibo_volume: 42
  dct_date: 2022^xs_gYear
  dct_identifier:
  - UT:000798210100003
  dct_isPartOf:
  - http://id.crossref.org/issn/0209-9683
  dct_language: eng
  dct_publisher: Springer Nature@
  dct_title: Even maps, the Colin de Verdière number and representations of graphs@
...