2 citations · 3 across the 10 of their papers we have counts for
6 papers · 1 filter
A Proof of the Linear Hadwiger Conjecture
Sergey Norin, Raphael Steiner
We show that there exists such that -minor free graphs are -colorable. The proof was found by GPT-6 Astra, following the directions by the authors.
Disproof of the dominating Hadwiger conjecture
Freddie Illingworth, Raphael Steiner
Hadwiger's conjecture (1943) states that every graph with chromatic number at least contains a -model: a collection of vertex-disjoint connected subgraphs $T_1,\do…
A relaxation of the Bermond-Thomassen conjecture
Stéphane Bessy, Matthijs Muis, Jean-Sébastien Sereni +2
The well-known Bermond-Thomassen conjecture states that every digraph of minimum out-degree at least contains vertex-disjoint directed cycles. Despite being posed in 198…
Disproof of the tree product conjecture via the Heisenberg group
Freddie Illingworth, Sergey Norin, Raphael Steiner
Product structure theory aims to understand complex graphs by embedding them into products of simpler graphs. In this direction, Campbell, Distel, Gollin, Harvey, Hendrey, Hickingb…
The Dominating 4-Colour Theorem
António Girão, Freddie Illingworth, Bojan Mohar +6
A "dominating -model" in a graph is a sequence of pairwise vertex-disjoint connected subgraphs of , such that whenever every vertex…
Long cycles in vertex transitive digraphs
Matija Bucić, Kevin Hendrey, Bojan Mohar +2
One of the most well-known conjectures concerning Hamiltonicity in graphs asserts that any sufficiently large connected vertex transitive graph contains a Hamilton cycle. In this f…