Cognitive radio is an emerging technology for the effective frequency utilization. The fixed spectrum allocation has resulted in spectrum holes. The cognitive radio solves the problem for unused spectrum by the mechanism of spectrum assignment. This paper proposes an efficient spectrum assignment by Markov scheduling, banker's algorithm for deadlock avoidance and applying the graph coloring problem for the fair allocation of resources. The CRN spectrum assignment problem is modeled using bi-graph and Markov analysis carried out has demonstrated to show the efficient scheduling and indicated the possible performance improvement in spectrum allocation/scheduling in CRN.