Let $G=(V,E)$ be a graph with no perfect matching. Then there exists a vertex $v$ such that every incident edge (i.e., every edge incident to $v$) is part of a maximum matching. I'm not sure how to prove this. How can every edge that coincides with $v$ be part of a maximum matching? It sou...
Self-factorial number is the number whose sum of factorial of digits is equal to the number itself. But there are only a few amount of them. For example; $$1=1!$$ $$2=2!$$ $$145= 1!+4!+5!$$ So what is the fourth self-factorial number? How about fifth?
What are the topics that should be mastered by someone who wants to understand geometric computational complexity? Surely, a lot of algebraic geometry and representation theory are needed, but which topics? and representation theory of what? groups, lie algebras etc? naming good resources ( text...
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