---
res:
  bibo_abstract:
  - "A k-subcolouring of a graph G is a function f : V (G) → {0,...,k − 1} such that
    the set of\r\nvertices coloured i induce a disjoint union of cliques. The subchromatic
    number, χsub(G),\r\nis the minimum k such that G admits a k-subcolouring. Nešetril,
    ˇ Ossona de Mendez,\r\nPilipczuk, and Zhu (2020), recently raised the problem
    of finding tight upper bounds for\r\nχsub(G2) when G is planar. We show that χsub(G2)
    ≤ 43 when G is planar, improving\r\ntheir bound of 135. We give even better bounds
    when the planar graph G has larger girth.\r\nMoreover, we show that χsub(G3) ≤
    95, improving the previous bound of 364. For these\r\nwe adapt some recent techniques
    of Almulhim and Kierstead (2022), while also extending\r\nthe decompositions of
    triangulated planar graphs of Van den Heuvel, Ossona de Mendez,\r\nQuiroz, Rabinovich
    and Siebertz (2017), to planar graphs of arbitrary girth. Note that these\r\ndecompositions
    are the precursors of the graph product structure theorem of planar graphs.\r\nWe
    give improved bounds for χsub(Gp) for all p ≥ 2, whenever G has bounded treewidth,\r\nbounded
    simple treewidth, bounded genus, or excludes a clique or biclique as a minor.\r\nFor
    this we introduce a family of parameters which form a gradation between the strong\r\nand
    the weak colouring numbers. We give upper bounds for these parameters for graphs\r\ncoming
    from such classes.\r\nFinally, we give a 2-approximation algorithm for the subchromatic
    number of graphs\r\nhaving a layering in which each layer has bounded cliquewidth
    and this layering is\r\ncomputable in polynomial time (like the class of all dth
    powers of planar graphs, for fixed\r\nd). This algorithm works even if the power
    p and the graph G is unknown.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Pedro P.
      foaf_name: Cortés, Pedro P.
      foaf_surname: Cortés
  - foaf_Person:
      foaf_givenName: Pankaj
      foaf_name: Kumar, Pankaj
      foaf_surname: Kumar
  - foaf_Person:
      foaf_givenName: Benjamin
      foaf_name: Moore, Benjamin
      foaf_surname: Moore
      foaf_workInfoHomepage: http://www.librecat.org/personId=6dc1a1be-bf1c-11ed-8d2b-d044840f49d6
  - foaf_Person:
      foaf_givenName: Patrice
      foaf_name: Ossona de Mendez, Patrice
      foaf_surname: Ossona de Mendez
  - foaf_Person:
      foaf_givenName: Daniel A.
      foaf_name: Quiroz, Daniel A.
      foaf_surname: Quiroz
  bibo_doi: 10.1016/j.disc.2024.114377
  bibo_issue: '4'
  bibo_volume: 348
  dct_date: 2025^xs_gYear
  dct_identifier:
  - UT:001401656900001
  dct_isPartOf:
  - http://id.crossref.org/issn/0012-365X
  dct_language: eng
  dct_publisher: Elsevier@
  dct_title: Subchromatic numbers of powers of graphs with excluded minors@
...