Now in these class notes, https://www.cs.umd.edu/class/spring2003/cmsc424-0401/ClassNotesMay1.ppt section Precedence Graph, it says

if the graph has a cycle, S is not serializable

But I think this is wrong and if the graph has a cycle, S is not conflict serializable and maybe be a serializable, because all serializable schedule is not conflict serializable?

Which of these is correct?

in other words, i mean Every conflict serializable schedule is serializable, but not all serializable schedules conflict-serializable. One way for testing of Conflict serializable is mentioned by using graph in: http://www.cburch.com/cs/340/reading/serial/index.html so if a graph has as cycle and not Conflict Serializable, maybe it means Serializable. am i right?

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