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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