Kahn--Lovász-type inequalities for graph factors

Abstract

The Kahn--Lovász theorem gives a sharp upper bound on the number of perfect matchings in a graph in terms of its degree sequence, extending the classical Brégman--Minc inequality for bipartite graphs. In this paper, we establish an asymptotically sharp extension of the Kahn--Lovász theorem to $F$-factors for every Hamiltonian graph $F$. As a consequence, we asymptotically determine the maximum number of $F$-factors in an $n$-vertex $m$-edge graph, yielding an $F$