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Hadwiger's conjecture, first formulated in 1943, is a vast generalization of the four-color theorem, and remains one of the central open problems in

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Exposé en anglais / Talk in english A simple greedy procedure shows that the chromatic number $\chi(G)$ of a graph $G$ is upper bounded by $\Delta(G)

The tree-independence number of a graph is the analogue of treewidth where, instead of minimising the size of bags, we minimise the size of a stable

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

We study biased Maker-Breaker games on a graph system {G1,…,Gs}, in which Maker's goal is to claim certain rainbow structures, i.e., specified

Using the Graph Minor Theorem, by Robertson and Seymour, one can easily prove that there are only a finite number of excluded minors for a given

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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