On the Delta(d)–chromatic number of a complete balanced multipartite graph

AP Burger, I Nieuwoudt, JH van Vuuren

Abstract


In this paper we solve (approximately) the problem of finding the minimum number of colours with which the vertices of a complete, balanced, multipartite graph G may be coloured such that the maximum degrees of all colour class induced subgraphs are at most some specified natural number d. The minimum number of colours in such a colouring is referred to as the Delta(d)–chromatic number of G. The problem of finding the Delta(d)–chromatic number of a complete, balanced, multipartite graph has its roots in an open graph theoretic characterisation problem and has applications conforming to the generic scenario where users of a system are in conflict if they require access to some shared resource. These conflicts are represented by edges in a so–called resource access graph, where vertices represent the users. An efficient resource access schedule is an assignment of the users to a minimum number of groups (modelled by means of colour classes) where some threshold d of conflict may be tolerated in each group. If different colours are associated with different time periods in the schedule, then the minimum number of groupings in an optimal resource access schedule for the above set of users is given by the Delta(d)–chromatic number of the resource access graph. A complete balanced multipartite resource access graph represents a situation of maximum conflict between members of different user groups of the system, but where no conflict occurs between members of the same user group (perhaps due to an allocation of diverse duties to the group members).


Full Text:

PDF


DOI: http://dx.doi.org/10.5784/23-1-45

Refbacks

  • There are currently no refbacks.

Comments on this article

View all comments





ISSN 2224-0004 (online); ISSN 0259-191X (print)

Powered by OJS and hosted by Stellenbosch University Library and Information Service since 2011.


Disclaimer:

This journal is hosted by the SU LIS on request of the journal owner/editor. The SU LIS takes no responsibility for the content published within this journal, and disclaim all liability arising out of the use of or inability to use the information contained herein. We assume no responsibility, and shall not be liable for any breaches of agreement with other publishers/hosts.

SUNJournals Help