Abstract
By a proper colouring of a simple graph, we mean an assignment of colours to its vertices with adjacent vertices receiving different colours. Applications of this graph‐theoretic modelling are numerous, especially in the areas of scheduling and timetabling. We shall refer to a proper colouration that uses a smallest possible number of colours as a minimum (proper) colouration. This number for the graph is simply its chromatic number, the determination of which is well known to be a ‘hard’ problem. In this paper, from the computational point of view of actually constructing a colouration, we examine a simple coalescence/expansion procedure that bases on the branch and bound technique improved by efficient bounding conditions. They include various tightened fathoming criteria as well as complete subgraph determination. For the computer implementation, we also look at the issues of branching rules and the decomposition of solution tree. With these efforts, empirical results show that minimum colourations can...
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Mathematical Education in Science and Technology
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
