Partition density, star arboricity, and sums of Laplacian eigenvalues of graphs

Alan Lew

Let $G=(V,E)$ be a graph on $n$ vertices, and let ${\lambda }_1(L(G))\ge \cdots \ge {\lambda }_{n-1}(L(G))\ge {\lambda }_n(L(G))=0$ be the eigenvalues of its Laplacian matrix $L(G)$. Brouwer conjectured that…