Owen D. Merkel

activity

20182021

collaborators

7 papers

math.CO2021

Mixing colourings in $2 K_{2}$ -free graphs

Carl Feghali, Owen Merkel

The reconfiguration graph for the $k$ -colourings of a graph $G$ , denoted $R_{k} (G)$ , is the graph whose vertices are the $k$ -colourings of $G$ and two colourings are joined by an e…

math.CO2021

Recolouring weakly chordal graphs and the complement of triangle-free graphs

Owen Merkel

For a graph $G$ , the $k$ -recolouring graph $R_{k} (G)$ is the graph whose vertices are the $k$ -colourings of $G$ and two colourings are joined by an edge if they differ in c…

math.CO2021

Colouring graphs with no induced six-vertex path or diamond

Jan Goedgebeur, Shenwei Huang, Yiao Ju +1

The diamond is the graph obtained by removing an edge from the complete graph on 4 vertices. A graph is ( $P_{6}$ , diamond)-free if it contains no induced subgraph isomorphic to a six…

cs.CG2020

Reconstructing a Polyhedron between Polygons in Parallel Slices

Therese Biedl, Pavle Bulatovic, Veronika Irvine +3

Given two $n$ -vertex polygons, $P = (p_{1}, \dots, p_{n})$ lying in the $x y$ -plane at $z = 0$ , and $P^{'} = (p_{1}^{'}, \dots, p_{n}^{'})$ lying in the $x y$ -plane at $z = 1$ , a banded surface is a triang…

cs.DM2020

Building a larger class of graphs for efficient reconfiguration of vertex colouring

Therese Biedl, Anna Lubiw, Owen Merkel

A $k$ -colouring of a graph $G$ is an assignment of at most $k$ colours to the vertices of $G$ so that adjacent vertices are assigned different colours. The reconfiguration graph of…

math.CO2018

An Optimal $χ$ -Bound for ( $P_{6}$ , diamond)-Free Graphs

Kathie Cameron, Shenwei Huang, Owen Merkel

Given two graphs $H_{1}$ and $H_{2}$ , a graph $G$ is $(H_{1}, H_{2})$ -free if it contains no induced subgraph isomorphic to $H_{1}$ or $H_{2}$ . Let $P_{t}$ be the path on $t$ vertices and $K_{t}$ b…

Mixing colourings in 2K2​-free graphs

Recolouring weakly chordal graphs and the complement of triangle-free graphs

Colouring graphs with no induced six-vertex path or diamond

Reconstructing a Polyhedron between Polygons in Parallel Slices

Building a larger class of graphs for efficient reconfiguration of vertex colouring

An Optimal χ-Bound for (P6​, diamond)-Free Graphs

Mixing colourings in $2 K_{2}$ -free graphs

An Optimal $χ$ -Bound for ( $P_{6}$ , diamond)-Free Graphs