Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Tuesday, April 12, 2022, 12:15 pm

**Duration**: 30 minutes

**Location**: OAT S15/S16/S17

**Speaker**: Raphael Steiner

In this talk, I will present some recent results on two variants of Hadwiger's conjecture. First, I will discuss the so-called Odd Hadwiger's conjecture, a strengthening of Hadwiger's conjecture proposed by Gerards and Seymour in 1995. First I will show a new upper bound for coloring graphs with no odd K_t-minor, thereby improving previous bounds for this problem, which comes along with a substantially simpler proof. Second, I will show a new bound of 2t-2 for clustered colorings of odd K_t-minor free graphs, in which we look for (possibly improper) colorings with monochromatic components of small size, this also significantly improves previous results. Third, I will discuss the so-called List Hadwiger's conjecture, which states that there exists a constant c such that every graph with no Kt-minor is ct-choosable (i.e., list colorable). I will present a new lower bound 2t-o(t) for list coloring K_t-minor free graphs which refutes a conjecture by Kawarabayashi and Mohar. Fourth, I will present a result saying that K_{s,t}-minor free graphs for large comparable s and t can have list chromatic number at least (1-o(1)(s+t+min(s,t)), this refutes a conjecture by Woodall.

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