On the notion of transversal of a sum of matroids
On the null space of a Colin de Verdière matrix
Let be a 3-connected planar graph, with . Let be a symmetric matrix with exactly one negative eigenvalue (of multiplicity 1), such that for with , if and are adjacent then and if and are nonadjacent then , and such that has rank . Then the null space of gives an embedding of in as follows: let be a basis of , and for let ; then , and embeds in such that connecting, for any two adjacent vertices , the points and by a shortest geodesic on , gives...
On the nullity of graphs.
On the number of 2-factors in rectangular lattice graphs.
On the number of antichains of finite power sets
On the number of complete subgraphs and circuits contained in graphs
On the number of cut-vertices in a graph.
On the number of cycles in a graph
On the number of cycles in -connected graphs.
On the number of derangements of a sharply k-ply transitive set of permutations.
On the number of descendants and ascendants in random search trees.
On the number of dissimilar pfaffian orientations of graphs
On the number of dissimilar pfaffian orientations of graphs
A subgraph H of a graph G is conformal if G - V(H) has a perfect matching. An orientation D of G is Pfaffian if, for every conformal even circuit C, the number of edges of C whose directions in D agree with any prescribed sense of orientation of C is odd. A graph is Pfaffian if it has a Pfaffian orientation. Not every graph is Pfaffian. However, if G has a Pfaffian orientation D, then the determinant of the adjacency matrix of D is the square of the number of perfect matchings of G. (See the book...
On the number of distributive lattices.
On the Number of Faces of Simplicial Complexes and the Purity of Frobenius.
On the number of fixed points for a continuous map of a finite connected graph.
On the number of forests
On the number of fully packed loop configurations with a fixed associated matching.
On the number of genus one labeled circle trees.
On the number of independent sets in a tree.