# eigenvalues

## The sum of the two largest eigenvalues ★★

Author(s): Gernert

Problem   Let be a graph on vertices and let be the eigenvalues of . Is ?

Keywords: eigenvalues; spectrum

## Alon-Saks-Seymour Conjecture ★★★

Author(s): Alon; Saks; Seymour

Conjecture   If is a simple graph which can be written as an union of edge-disjoint complete bipartite graphs, then .

## Fowler's Conjecture on eigenvalues of (3,6)-polyhedra ★★

Author(s): Fowler

Conjecture   Let be the graph of a -polyhedron with vertices. Then the eigenvalues of can be partitioned into three classes: , (where is nonnegative for ), and .

Keywords: (3,6)-polyhedron; eigenvalues