Siani Smith

collaborators

4 papers

math.CO2021

Disjoint Paths and Connected Subgraphs for H-Free Graphs

Walter Kern, Barnaby Martin, Daniël Paulusma +2

The well-known Disjoint Paths problem is to decide if a graph contains k pairwise disjoint paths, each connecting a different terminal pair from a set of k distinct pairs. We deter…

cs.DS2021

Acyclic, Star, and Injective Colouring: Bounding the Diameter

Christoph Brause, Petr Golovach, Barnaby Martin +3

We examine the effect of bounding the diameter for well-studied variants of the Colouring problem. A colouring is acyclic, star, or injective if any two colour classes induce a for…

math.CO2021

Colouring Graphs of Bounded Diameter in the Absence of Small Cycles

Barnaby Martin, Daniel Paulusma, Siani Smith

For $k \geq 1$ , a $k$ -colouring $c$ of $G$ is a mapping from $V (G)$ to ${1, 2, \dots, k}$ such that $c (u) \neq = c (v)$ for any two non-adjacent vertices $u$ and $v$ . The $k$ -Colouring…

cs.CC2020

Hard Problems That Quickly Become Very Easy

Barnaby Martin, Daniël Paulusma, Siani Smith

A graph class is hereditary if it is closed under vertex deletion. We give examples of NP-hard, PSPACE-complete and NEXPTIME-complete problems that become constant-time solvable fo…