LIPIcs.MFCS.2023.1.pdf
- Filesize: 391 kB
- 2 pages
Document
Exploring the Space of Colourings with Kempe Changes (Invited Talk)
Author
Marthe Bonamy 
-
Part of:
Volume:
48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Mathematical Foundations of Computer Science (MFCS) - License:
Creative Commons Attribution 4.0 International license
- Publication date: 2023-08-21
File
Document Identifiers
Author Details
Cite AsGet BibTex
Marthe Bonamy. Exploring the Space of Colourings with Kempe Changes (Invited Talk). In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 1:1-1:2, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.MFCS.2023.1
https://doi.org/10.4230/LIPIcs.MFCS.2023.1
Abstract
Kempe changes were introduced in 1879 in an attempt to prove the 4-colour theorem. They are a convenient if not crucial tool to prove various colouring theorems. Here, we consider how to navigate from a colouring to another through Kempe changes. When is it possible? How fast?
Subject Classification
ACM Subject Classification
- Mathematics of computing → Graph coloring
Keywords
- Graph theory
- graph coloring
- reconfiguration
Metrics
- Access Statistics
-
Total Accesses (updated on a weekly basis)
0PDF Downloads
References
-
Kenneth Appel and Wolfgang Haken. The solution of the four-color-map problem. Scientific American, 237(4):108-121, 1977.
-
Armen S. Asratian and Carl Johan Casselgren. Solution of Vizing’s problem on interchanges for the case of graphs with maximum degree 4 and related results. Journal of Graph Theory, 82(4):350-373, 2016.
-
Marthe Bonamy, Oscar Defrain, Tereza Klimošová, Aurélie Lagoutte, and Jonathan Narboni. On vizing’s edge colouring question. Journal of Combinatorial Theory, Series B, 159:126-139, 2023.
-
Alfred B. Kempe. On the geographical problem of the four colours. American journal of mathematics, 2(3):193-200, 1879.
-
Jessica McDonald, Bojan Mohar, and Diego Scheide. Kempe equivalence of edge-colorings in subcubic and subquartic graphs. Journal of Graph theory, 70(2):226-239, 2012.
-
Jonathan Narboni. Vizing’s edge-recoloring conjecture holds. arXiv preprint arXiv:2302.12914, 2023.
-
Vadim G. Vizing. On an estimate of the chromatic class of a p-graph. Discret Analiz, 3:25-30, 1964.
-
Vadim G. Vizing. Some unsolved problems in graph theory. Russian Mathematical Surveys, 23(6):125, 1968.