Proving Clique Number of a Regular Graph
سؤال
I am very new to Graph Theory and I am trying to prove the following statement from a problem set for my class:
Prove that if G is a regular graph on n vertices $(n \ge 2)$, then $\omega(G) \in \{1, 2, 3,... \lfloor n / 2 \rfloor, n\}$
I am confused by the part where it places the clique number to be in this set: $\omega(G) \in \{1, 2, 3,... \lfloor n / 2 \rfloor, n\}$. Why can the clique number be only in the first half of this set (or it can be n) and why can't it be anything between $\lfloor n / 2 \rfloor$ and $ n$?
How can I go about proving this claim? Any tips would be appreciated.
لا يوجد حل صحيح
لا تنتمي إلى cs.stackexchange