Cognitive radio is one of the technologies promoting flexible and efficient use of radio frequency spectrum, thus solving spectrum scarcity problem. Frequency assignment is an integral part of the cognitive radio spectrum management and a critical point of success or failure of the cognitive radio concept. In this paper, cognitive radio frequency assignment with a novel interference weighting and categorization is proposed, as an extension of the solution to the graph coloring problem. In our approach, the edge weights quantifying the interference potential are appended to the conflict graph, co-and adjacent channel interference are treated, and dynamically changing local lists of blocked frequencies are included. We propose the improved cognitive radio saturation metric for the dynamic vertex ordering and to introduce interference categorization which will reduce the communication overhead. Using the proposed model, resource manager can quantify individual interference components, as well as aggregate interference from multiple users, resulting in more knowledgeable frequency decisions. Generalization of the proposed model is suggested. The suggested generalization consists of the selection of the central frequency and optimal bandwidth to be used, according to the user requirements. We have developed interference-sensitive algorithms for minimizing the interference and maximizing the throughput, both in centralized and distributed implementation. The results show significant reduction of the interference, improved spectrum efficiency, and increase in network throughput, comparing to the benchmark algorithms.