In cellular networks, channels must be assigned to call requests so that interference constraints are respected and bandwidth is minimized. The number of call requests per cell is continually changing, making channel assignment naturally an online problem. We describe two new online channel assignment algorithms for networks based on a regular hexagonal layout of cells, where interference levels depend only on the distance between cells. Such networks can be modelled by so-called hexagon graphs. Our model incorporates different separation constraints, prescribed minimal differences between channels assigned to cells within a certain distance of each other. The algorithms presented are the first to take into account separation constraints between non-adjacent cells in this type of layout. The algorithms are distributed in nature: each cell server will need only a limited exchange of information with cells in its proximity to make decisions on its channel assignment.