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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
In order to further develop the theory of packing trees and packing forests in an undirected graph, we extended the notion of supermodular functions
In the first paper of the Graph Minors series [JCTB ’83], Robertson and Seymour proved the Forest Minor theorem: the H-minor-free graphs have bounded
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
A triangulation of a surface is k-irreducible if every edge belongs to a non-contractible curve of length k and there are no shorter non-contractible
We will look at an analogue theorem of the classical Erdős-Pósa Theorem. We prove a $GF(q)$-representable matroid analogue of Robertson and Seymour's
A central concept in social choice theory is that of a Condorcet winner: an outcome that defeats every alternative in a pairwise majority vote. While