---
res:
  bibo_abstract:
  - 'The inertia bound and ratio bound (also known as the Cvetković bound and Hoffman
    bound) are two fundamental inequalities in spectral graph theory, giving upper
    bounds on the independence number a(G) of a graph G in terms of spectral information
    about a weighted adjacency matrix of G. For both inequalities, given a graph G,
    one needs to make a judicious choice of weighted adjacency matrix to obtain as
    strong a bound as possible. While there is a well‐established theory surrounding
    the ratio bound, the inertia bound is much more mysterious, and its limits are
    rather unclear. In fact, only recently did Sinkovic find the first example of
    a graph for which the inertia bound is not tight (for any weighted adjacency matrix),
    answering a longstanding question of Godsil. We show that the inertia bound can
    be extremely far from tight, and in fact can significantly underperform the ratio
    bound: for example, one of our results is that for infinitely many n, there is
    an n‐vertex graph for which even the unweighted ratio bound can prove a(G)<4n^3/4,
    but the inertia bound is always at least n/4. In particular, these results address
    questions of Rooney, Sinkovic, and Wocjan–Elphick–Abiad.@eng'
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Matthew
      foaf_name: Kwan, Matthew
      foaf_surname: Kwan
  - foaf_Person:
      foaf_givenName: Yuval
      foaf_name: Wigderson, Yuval
      foaf_surname: Wigderson
      foaf_workInfoHomepage: http://www.librecat.org/personId=2d0023a0-1567-11f0-833d-d5c1e476d4b5
  bibo_doi: 10.1112/blms.13127
  bibo_issue: '10'
  bibo_volume: 56
  dct_date: 2024^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0024-6093
  - http://id.crossref.org/issn/1469-2120
  dct_language: eng
  dct_publisher: Wiley@
  dct_title: The inertia bound is far from tight@
...