6 papers · 1 filter
Optimal b-Colourings and Fall Colourings in -Free Graphs
Jungho Ahn, Tala Eagling-Vose, Felicia Lucke +3
In a colouring of a graph, a vertex is b-chromatic if it is adjacent to a vertex of every other colour. We consider four well-studied colouring problems: b-Chromatic Number, Tight…
On Detecting -Induced Minors for Small
Tala Eagling-Vose, Barnaby Martin, Daniël Paulusma +1
We consider the -Induced Minor problem: for a fixed graph~, decide whether a given graph contains as an induced minor. While the problem is known to be NP-complete fo…
Steiner Forest for -Subgraph-Free Graphs
Tala Eagling-Vose, David C. Kutner, Felicia Lucke +4
Our main result is a full classification, for every connected graph , of the computational complexity of Steiner Forest on -subgraph-free graphs. To obtain this dichotomy, we…
Colouring Graphs Without a Subdivided H-Graph: A Full Complexity Classification
Tala Eagling-Vose, Jorik Jooken, Felicia Lucke +2
We consider Colouring on graphs that are -subgraph-free for some fixed graph , which are graphs that do not contain as a subgraph. To classify the complexity of Colouring…
Complexity Framework For Forbidden Subgraphs V: Beyond Simple Graphs
Tala Eagling-Vose, Barnaby Martin, Daniel Paulusma +1
We continue the study of the recently-introduced C123-framework, for (simple) graph problems restricted to inputs specified by the forbidding of some finite set of subgraphs, to mo…
Finding d-Cuts in Claw-free Graphs
Jungho Ahn, Tala Eagling-Vose, Felicia Lucke +2
The Matching Cut problem is to decide if the vertex set of a connected graph can be partitioned into two non-empty sets and such that the edges between and form a m…