Schedules that are serialisable

How can I make a serializable schedule?
Ik a schedule is serializable if it can be converted to a serial schedule by a sequence of non-conflicting swaps of actions. I’ve been disputing with the academics for a long time, but they insist on using the term from that said in this article.
Could you kindly point out where I’m going wrong? Is it possible to have a schedule that cannot be converted to a serial schedule but is still serial?
Thank you.

I think this is a question that you should ask your database vendor. Usually, when you use the transaction isolation level SERIALIZABLE on all your JDBC connections, it will be guaranteed that transactions which successfully commit are scheduled in a way that essentially equates to serial execution/scheduling, though you have to understand that many transactions could fail in-flight due to that for “no apparent reason”.