In recent years, channel-hopping-based medium access control protocols have been proposed to improve the capacity in a decentralized multichannel cognitive radio (CR) network without using extra control channels. Each CR user has to stochastically follow a default channel-hopping sequence in order to locate a channel and conduct its frame transmission. In this paper, theoretical analysis is conducted on the probability of channel availability and the average frame delay for primary users (PUs) by considering the impact caused by imperfect sensing of CR users and imperfect synchronization between the primary and CR networks. According to the proposed analytical model with realistic considerations, an optimal channel-hopping sequence (OCS) approach is designed for the CR users based on a dynamic programming technique. It is designed by exploiting the optimal load balance between channel availability and channel utilization within the delay constraints of PUs. By adopting the OCS approach, maximum aggregate throughput of CR users can be achieved while considering PU's quality-of-service (QoS) requirements. Moreover, in addition to the paired CR networks, the logical partition problem that occurs in generalized CR networks will also be addressed. This problem can severely degrade the aggregate throughput due to the decreased probability of connectivity between CR users, especially in a CR network with heavy traffic. Therefore, both wake-up successive contention (WSC) and wake-up counter-reset successive contention (WCSC) algorithms are proposed to increase the number of negotiations by both exploring the blind spot of imperfect sensing and amending the contention mechanisms between CR users. Compared to conventional channel-hopping sequences, numerical results illustrate that the proposed approaches can effectively maximize aggregate throughput for CR users under the QoS requirements of PUs.