12 papers
Two Relaxations of the Dominating Hadwiger's Conjecture
António Girão, Sergey Norin, Youri Tamitegama +1
Illingworth and Wood recently proposed the Dominating Hadwiger's Conjecture, a strengthening of Hadwiger's Conjecture which asserts that every graph with no dominating -model…
Non-Homotopic Drawings of Multigraphs
António Girão, Freddie Illingworth, Alex Scott +1
A multigraph drawn in the plane is non-homotopic if no two edges connecting the same pair of vertices can be continuously deformed into each other without passing through a vertex,…
On -factors of Hamiltonian graphs
Alberto Espuny DÃaz, António Girão, Bertille Granet +1
Let . We show that, for a sufficiently small , any sufficiently large -vertex Hamiltonian graph of minimum degree at least contains a…
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…
Induced subdivisions of in graphs of high girth
António Girão, Zach Hunter
In this paper, we show that for all , every graph with minimum degree and girth at least contains an induced subdivision of a . This answers a probl…
Blowups of triangle-free graphs
António Girão, Zach Hunter, Yuval Wigderson
A highly influential result of Nikiforov states that if an -vertex graph contains at least copies of a fixed -vertex graph , then contains a blowup of …