Is there a lower bound on the number of perfect matchings in a $k$-regular bipartite graph? One can use Hall's marriage theorem and induction on $k$ to derive the lower bound of $k$. I can't come up ...
Does anybody know if there is any research on a lower bound on the number of (non-isomorphic) unlabeled planar graphs with maximum node degree $d$? Alternatively, a lower bound on the number of all ...
I am trying to find a good lower bound for chromatic number of one family of graphs. I'm curious what are the known lower bounds for chromatic number. There are two obvious: $\chi(G) \geq \omega(G)$ ...