Tight lower bounds on the matching number in a graph with given maximum degree

Michael A. Henning, Anders Yeo

Let $k\ge 3$. We prove the following three bounds for the matching number, ${\alpha }^{\prime }(G)$, of a graph, $G$, of order $n$ size $m$ and maximum degree at most $k$. If $k$ is odd, then $α'…