What is perfect elimination bipartite graph?

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I am not a Maths guy, and I was required to read a paper on Graph Theory. Now after few pages the definition of perfect elimination bipartite graph comes up, no matter how hard I try grasp the meaning I could not put it together. Heres the definition Definition I understand individual parts but couldn't put it together. Too many abstract symbols and I couldn't find anything google too. Can anyone please what it is actually in simpler words with example.

Thank you.