Channel assignment is an important step in communication networks. The objectives of minimizing networks interference and the channels used are the problems in the channel assignments of the networks. In real environments, some difference will be expected in the performance of the networks when the channel allocation algorithms under more accurate interference models are deployed. In this research, the wireless mesh networks represent dynamic networks while static networks are represented by the cellular networks. In the wireless mesh networks, communication between a pair of nodes happens when both nodes are assigned with channels. The cellular networks are the radio network distributed over land areas called cells, each served by at least one fixed-location transceiver. Channel assignments in the networks is an application of the vertex coloring in graph theory. Previously, the Greedy Algorithm was used for link scheduling but only the adjacent channel constraint was considered. Here, an algorithm called Improved Greedy Algorithm was proposed to solve the channel assignments by considering the adjacent channel and co-channel constraints which is an improvement to the algorithm. Besides, Simulated Annealing and T-coloring problem are combined to minimize the channels used. The algorithms are applied for single and multiple channels communications in the wireless mesh networks and cellular networks to show the different results of the channel assignments. Further improvement is made on the multiple channels case where the Improved Greedy Algorithm is applied by considering the cosite constraint in addition to the co-channel and adjacent channel constraints. The Improved Greedy Algorithm has been tested in a series of simulations. Results for the simulations prove that the Improved Greedy Algorithm perform significantly well for the channel assignment problem
