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1. The Complexity of Two Colouring Games

   We consider two variants of orthogonal colouring games on graphs. In these games, two players alternate colouring uncoloured vertices (from a choice...

   Stephan Dominique Andres, François Dross, ... Richard J. Nowakowski in Algorithmica

   Article Open access 24 November 2022
   

2. Star Colouring of Regular Graphs Meets Weaving and Line Graphs

   For \( q\in \mathbb {N} \) , a...

   M. A. Shalu, Cyriac Antony in Algorithms and Discrete Applied Mathematics

   Conference paper 2024
   

3. Guide to Graph Colouring Algorithms and Applications

   This textbook treats graph colouring as an algorithmic problem, with a strong emphasis on practical applications. The author describes and analyses...

   R. M. R. Lewis in Texts in Computer Science

   Textbook 2021
   

4. NP-Completeness and One Polynomial Subclass of the Two-Step Graph Colouring Problem

   Abstract

   This paper considers the two-step colouring problem for an undirected connected graph. The problem is about colouring the graph in a given...

   N. S. Medvedeva, A. V. Smirnov in Automatic Control and Computer Sciences

   Article 01 December 2020
   

5. Advanced Techniques for Graph Colouring

   In this chapter, we review many of the algorithmic techniques that can be used for the graph colouring problem. The intention is to give the reader...

   R. M. R. Lewis in Guide to Graph Colouring

   Chapter 2021
   

6. Graph Modification for Edge-Coloured and Signed Graph Homomorphism Problems: Parameterized and Classical Complexity

   We study the complexity of graph modification problems with respect to homomorphism-based colouring properties of edge-coloured graphs. A...

   Florent Foucaud, Hervé Hocquard, ... Théo Pierron in Algorithmica

   Article 04 January 2022
   

7. Linear-Time Graph Programs for Unbounded-Degree Graphs

   Achieving the complexity of graph algorithms in conventional languages with programs based on graph transformation rules is challenging because of...

   Ziad Ismaili Alaoui, Detlef Plump in Graph Transformation

   Conference paper 2024
   

8. Introduction to Graph Colouring

   In mathematics, a graph can be thought of as a set of objects in which some pairs of objects are connected by links. The interconnected objects are...

   R. M. R. Lewis in Guide to Graph Colouring

   Chapter 2021
   

9. Reducing Graph Parameters by Contractions and Deletions

   We consider the following problem: for a given graph G and two integers k and d , can we apply a fixed graph operation at most k times in order to...

   Felicia Lucke, Felix Mann in Algorithmica

   Article Open access 09 July 2023
   

10. Graph Theory

    This chapter discusses graph theory where a graph G = (V, E) consists of vertices and edges. It is a practical branch of mathematics that deals with...

    Gerard O’Regan in Mathematical Foundations of Software Engineering

    Chapter 2023
    

11. Injective Colouring for H-Free Graphs

    A function \(c:V(G)\rightarrow \{1,2,\ldots ,k\}\)...

    Jan Bok, Nikola Jedličková, ... Siani Smith in Computer Science – Theory and Applications

    Conference paper 2021
    

12. 3-Colouring \(P_t\)-Free Graphs Without Short Odd Cycles

    Alberto Rojas Anríquez, Maya Stein in Algorithmica

    Article 17 October 2022

13. The Complexity of Star Colouring in Bounded Degree Graphs and Regular Graphs

    A k-star colouring of a graph G is a function $$f:V(G)\rightarrow...

    M. A. Shalu, Cyriac Antony in Algorithms and Discrete Applied Mathematics

    Conference paper 2022
    

14. Colouring Graphs of Bounded Diameter in the Absence of Small Cycles

    For \(k\ge 1\) , a k-colouring c of...

    Barnaby Martin, Daniël Paulusma, Siani Smith in Algorithms and Complexity

    Conference paper 2021
    

15. On the Complexity of Colouring Antiprismatic Graphs

    A graph G is prismatic if for every triangle T of G , every vertex of G not in T has a unique neighbour in T . The complement of a prismatic graph is...

    Myriam Preissmann, Cléophée Robin, Nicolas Trotignon in Algorithmica

    Article 18 September 2020
    

16. Colouring Graphs with No Induced Six-Vertex Path or Diamond

    The diamond is the graph obtained by removing an edge from the complete graph on 4 vertices. A graph is (...

    Jan Goedgebeur, Shenwei Huang, ... Owen Merkel in Computing and Combinatorics

    Conference paper 2021
    

17. Quantum Circuit Compilation for the Graph Coloring Problem

    In this work we investigate the performance of greedy randomised search (GRS) techniques to the problem of compiling quantum circuits that solve...

    Angelo Oddi, Riccardo Rasconi, ... Hamish Beck in AIxIA 2022 – Advances in Artificial Intelligence

    Conference paper 2023
    

18. Deterministic Graph-Walking Program Mining

    Owing to their versatility, graph structures admit representations of intricate relationships between the separate entities comprising the data. We...

    Peter Belcak, Roger Wattenhofer in Advanced Data Mining and Applications

    Conference paper 2022
    

19. Colouring (P_r + P_s)-Free Graphs

    The k -Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a fixed integer  k such that no two...

    Tereza Klimošová, Josef Malík, ... Veronika Slívová in Algorithmica

    Article Open access 25 January 2020
    

20. Colouring simplicial complexes via the Lechuga–Murillo’s model

    Lechuga and Murillo showed that a non-oriented, simple, connected, finite graph G is k -colourable if and only if a certain pure Sullivan algebra...

    David Méndez in Applicable Algebra in Engineering, Communication and Computing

    Article Open access 12 June 2020