• Corpus ID: 239015879

Improved lower bound for the list chromatic number of graphs with no $K_t$ minor

  title={Improved lower bound for the list chromatic number of graphs with no \$K\_t\$ minor},
  author={Raphael Steiner},
Hadwiger’s conjecture asserts that every graph without a Kt-minor is (t − 1)colorable. It is known that the exact version of Hadwiger’s conjecture does not extend to list coloring, but it has been conjectured by Kawarabayashi and Mohar (2007) that there exists a constant c such that every graph with no Kt-minor has list chromatic number at most ct. More specifically, they also conjectured that this holds for c = 3 2 . Refuting the latter conjecture, we show that the maximum list chromatic… 


A relaxed Hadwiger's Conjecture for list colorings
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Connectivity and choosability of graphs with no K minor
In 1943, Hadwiger conjectured that every graph with no $K_t$ minor is $(t-1)$-colorable for every $t\ge 1$. While Hadwiger's conjecture does not hold for list-coloring, the linear weakening is
Further Progress towards the List and Odd Versions of Hadwiger's Conjecture.
In 1943, Hadwiger conjectured that every graph with no $K_t$ minor is $(t-1)$-colorable for every $t\ge 1$. In the 1980s, Kostochka and Thomason independently proved that every graph with no $K_t$
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  • D. Wood
  • Mathematics, Computer Science
    Eur. J. Comb.
  • 2010
The main ingredients in the proof are a list colouring argument due to Kawarabayashi and Mohar, a recent result of Norine and Thomas that says that every sufficiently large (t+1)-connected graph contains a K"t-minor, and a new sufficient condition for a graph to have a set of edges whose contraction increases the connectivity.
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Disproof of the List Hadwiger Conjecture
The List Hadwiger Conjecture is disproved by constructing a-minor-free graph that is not $4t-choosable for every integer $t\geq 1$.
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  • L. Postle
  • Mathematics, Computer Science
  • 2020
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Hadwiger's Conjecture
  • P. Seymour
  • Computer Science, Mathematics
    Open Problems in Mathematics
  • 2016
This is a survey of Hadwiger’s conjecture from 1943, that for all t ≥ 0, every graph either can be t-coloured, or has a subgraph that can be contracted to the complete graph on t + 1 vertices. This
List colourings of planar graphs
  • M. Voigt
  • Computer Science
    Discret. Math.
  • 1993
A graph G is k-choosable if all lists L(u) have the cardinality k and G is L-list colourable for all possible assignments of such lists.