Raphael Steiner, Strengthening Hadwiger’s conjecture for 4- and 5-chromatic graphs

Room B332 IBS (기초과학연구원)

Hadwiger's famous coloring conjecture states that every t-chromatic graph contains a $K_t$-minor. Holroyd conjectured the following strengthening of Hadwiger's conjecture: If G is a t-chromatic graph and S⊆V(G) takes all colors in every t-coloring of G, then G contains a $K_t$-minor rooted at S. We prove this conjecture in the first open case of t=4.

Robert Hickingbotham, Treewidth, Circle Graphs and Circular Drawings

Zoom ID: 869 4632 6610 (ibsdimag)

A circle graph is an intersection graph of a set of chords of a circle. In this talk, I will describe the unavoidable induced subgraphs of circle graphs with large treewidth. This includes examples that are far from the `usual suspects'. Our results imply that treewidth and Hadwiger number are linearly tied on the class

Meike Hatzel, Fixed-Parameter Tractability of Directed Multicut with Three Terminal Pairs Parametrised by the Size of the Cutset: Twin-Width Meets Flow-Augmentation

Room B332 IBS (기초과학연구원)

We show fixed-parameter tractability of the Directed Multicut problem with three terminal pairs (with a randomized algorithm). This problem, given a directed graph $G$, pairs of vertices (called terminals) $(s_1,t_1)$, $(s_2,t_2)$, and $(s_3,t_3)$, and an integer $k$, asks to find a set of at most $k$ non-terminal vertices in $G$ that intersect all $s_1t_1$-paths, all

Daniel Altman, TBA

Zoom ID: 224 221 2686 (ibsecopro)

Stijn Cambie, Recent progress on the Union-closed conjecture and related

Room B332 IBS (기초과학연구원)

We give a summary on the work of the last months related to Frankl's Union-Closed conjecture and its offsprings. The initial conjecture is stated as a theorem in extremal set theory; when a family F is union-closed (the union of sets of F is itself a set of $\mathcal F$), then $\mathcal F$ contains an

István Tomon, Configurations of boxes

Room B332 IBS (기초과학연구원)

Configurations of axis-parallel boxes in $\mathbb{R}^d$ are extensively studied in combinatorial geometry. Despite their perceived simplicity, there are many problems involving their structure that are not well understood. I will talk about a construction that shows that their structure might be more complicated than people conjectured.

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