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In 1943, Hadwiger conjectured that every k-chromatic graph has a K_k-minor. While the cases k = 5 and k = 6 have been shown to be equivalent to the
Strong flip-flatness has emerged as a natural dense analogue of uniform almost-wideness in the context of preservation theorems, but its combinatorial
A graph is reconstructible if it is determined up to isomorphism by the multiset of its proper induced subgraphs. The reconstruction conjecture
The celebrated Linear Arboricity Conjecture of Akiyama, Exoo, and Harary from 1980 asserts that the edges of every graph with maximum degree Δ can be