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

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, October 12, 2023, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Raphael Steiner

Scott and Seymour conjectured the existence of a function f:N→N such that, for every graph G and tournament T on the same vertex set, χ(G)⩾f(k) implies that χ(G[N+T(v)])⩾k for some vertex v. In this note we disprove this conjecture even if v is replaced by a vertex set of size O(log |V(G)|). As a consequence, we answer in the negative a question of Harutyunyan, Le, Thomassé, and Wu concerning the corresponding statement where the graph G is replaced by another tournament, and disprove a related conjecture of Nguyen, Scott, and Seymour. We also show that the setting where chromatic number is replaced by degeneracy exhibits a quite different behaviour. Based on joint work with Girao, Illingworth, Hendrey, Lehner, Michel and Savery.

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