• Corpus ID: 239015879

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

@inproceedings{Steiner2021ImprovedLB,
title={Improved lower bound for the list chromatic number of graphs with no \$K\_t\$ minor},
author={Raphael Steiner},
year={2021}
}
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…

## References

SHOWING 1-10 OF 25 REFERENCES
A relaxed Hadwiger's Conjecture for list colorings
• Computer Science, Mathematics
J. Comb. Theory, Ser. B
• 2007
It is shown that there exists a computable constant f(k) such that any graph G without K"k as a minor admits a vertex partition V"1,...,V"@?"1"5"."5"k"@? such that each component in the subgraph induced on V"i (i>=1) has at most f( k) vertices.
Connectivity and choosability of graphs with no K minor
• Mathematics
• 2020
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 $K_t$
• 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.
• Computer Science, Mathematics
Comb.
• 1993
It is shown (without assuming the 4CC) that every minimal counterexample to Hadwiger's conjecture whent=5 is “apex”, that is, it consists of a planar graph with one additional vertex.
Disproof of the List Hadwiger Conjecture
• Computer Science, Mathematics
Electron. J. Comb.
• 2011
The List Hadwiger Conjecture is disproved by constructing a-minor-free graph that is not $4t-choosable for every integer$t\geq 1$. Further progress towards Hadwiger's conjecture • L. Postle • Mathematics, Computer Science ArXiv • 2020 It is shown in this paper that every graph with no$K_t$minor is$O(t (\log t)^{\beta})$-colorable for every$\beta > 0\$.
Lower bound of the hadwiger number of graphs by their average degree
The aim of this paper is to show that the minimum Hadwiger number of graphs with average degreek isO(k/√logk). Specially, it follows that Hadwiger’s conjecture is true for almost all graphs withn