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

Tuesday, February 14, 2023 @ 4:30 PM - 5:30 PM KST

Room B332, IBS (기초과학연구원)

Hadwiger’s famous coloring conjecture states that every t-chromatic graph contains a $K_t$-minor. Holroyd [Bull. London Math. Soc. 29, (1997), pp. 139-144] 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. Notably, our result also directly implies a stronger version of Hadwiger’s conjecture for 5-chromatic graphs as follows: Every 5-chromatic graph contains a $K_5$-minor with a singleton branch-set. In fact, in a 5-vertex-critical graph we may specify the singleton branch-set to be any vertex of the graph. Joint work with Anders Martinsson (ETH).


Tuesday, February 14, 2023
4:30 PM - 5:30 PM KST
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Room B332
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Sang-il Oum (엄상일)
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IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
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IBS Discrete Mathematics Group (DIMAG)
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