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Title:  Highly connected minors in k-chromatic graphs

Abstract: One of the deepest problems in graph theory is Hadwiger's Conjecture, which asserts that every k-chromatic graph contains a clique minor of order k for each positive integer k. The conjecture is confirmed to be true when k is at most 6, and in fact, it is equivalent to the Four Color Theorem when k equals 5 or 6, and remains wide open for k at least 7. In this talk, we will explore a weaker version of the conjecture: what's the function f(k) so that an f(k)-chromatic graph contains a k-connected minor? No prior knowledge in graph theory will be assumed in this talk. This is based on joint work with Runrun Liu and Martin Rolek.

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Gexin Yu

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