The constitution of India doesn't explicitly require that any minister of the council of ministers of a state should hold any portfolio. So this is applicable to the chief minister too. But, there are a certain set of portfolios which various chief ministers in Kerala have held in common, namely, the Home department, and General Administration. The Home department is usually controlled by the chief minister because it controls the Police Department of the state. This is largely because, the Police system is considered in post-British India as a power enforcing tool rather than an instrument for service. Hence whoever holds power would like to have control over the Police department. In the history of Kerala, certain chief ministers had to allow other minister to handle the Home department owing to the power equations of party/coalition politics.
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