2 citations · 4 across the 8 of their papers we have counts for
8 papers
On unknotting tunnel systems of satellite chain links
Darlan Girão, João M. Nogueira, António Salgueiro
We prove that the tunnel number of a satellite chain link with a number of components higher than or equal to twice the bridge number of the companion is as small as possible among…
Cycle convexity and the tunnel number of links
Júlio Araújo, Victor Campos, Darlan Girão +3
In this work, we introduce a new graph convexity, that we call Cycle Convexity, motivated by related notions in Knot Theory. For a graph , define the interval function in…
On links minimizing the tunnel number
Darlan Girão, João M. Nogueira, António Salgueiro
We show a combinatorial argument in the diagram of large class of links, including satellite and hyperbolic links, where for each of which the tunnel number is the minimum possible…
State graphs and fibered state surfaces
Darlan Girão, Jessica S. Purcell
Associated to every state surface for a knot or link is a state graph, which embeds as a spine of the state surface. A state graph can be decomposed along cut-vertices into graphs…
Fiber surfaces from alternating states
Darlan Girão, João M. Nogueira, António Salgueiro
In this paper we define alternating Kauffman states of links and we characterize when the induced state surface is a fiber. In addition, we give a different proof of a similar theo…
Rank gradient of small covers
Darlan Girão
We prove that if is a small cover of a compact right-angled hyperbolic polyhedron then admits a cofinal tower of finite sheeted covers with positive r…