# Minus definition in Diestel's Graph Theory (3rd ed.)

by Gogis   Last Updated August 03, 2019 15:20 PM

In Diestel's Graph Theory book (3rd ed.) on page $$11$$, we have a graph $$G = (V, E)$$ and $$X \subseteq V \cup E$$. We then use the graph $$G-X$$ in the reasoning, however, the $$-$$ operator was defined in the book specifically for cases when $$X \subseteq V$$ or $$X \subseteq E$$ (page $$4$$).

Therefore, how should I interpret $$G-U$$ when $$X \cap V \neq \emptyset \land X \cap E \neq \emptyset$$? I thought of $$2$$ possibilities:

1. The first one is to intuitively understand it and expand the definition of $$-$$ by yourself, however, this does not fit into the rigorous nature of the book.

2. The second option is that the $$-$$ is sort of an extension of the $$-$$ from set theory. That way we have $$X \cap V = A$$, $$X \cap E = B$$ and $$G-X = G - (A \cup B) = (G - A) \cap (G - B)$$, although even in this case I would expect some notion about it in the textbook.

I am probably just missing some trivial detail(s), but since I exhausted my options, I made it into a question here.

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