Raphael Steiner, Congruence-constrained subdivisions in digraphs

Zoom ID: 869 4632 6610 (ibsdimag)

I will present the short proof from that for every digraph F and every assignment of pairs of integers $(r_e,q_e)_{e\in A(F)}$ to its arcs, there exists an integer $N$ such that every digraph D with dichromatic number at least $N$ contains a subdivision of $F$ in which $e$ is subdivided into a directed path of

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.

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