The problem of adaptive multicolouring is finding a multicolouring for a graph and each of a sequence of changing weight vectors. Recolouring is either not allowed at all, or is allowed only in limited amounts. The aim is to minimize the number of colours used, subject to certain restrictions on the weight vectors. We establish the number of colours needed for adaptive multicolouring for the class of k-colourable graphs, both for the case when no recolouring is allowed, and for a case where limited recolouring is allowed. Subject Classification (1991): 05C15 * This work was partially financed by the FCAR-BNR-CRSNG project "Méthodes mathématiques pour la synthèse des systèmes informatiques."
Mathematics