We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdős and Rényi about perfect matchings in random bipartite graphs. We also present an application to commutative graphs, a class of graphs that are featured in additive number theory.

A latin transversal in a square matrix of order n is a set of entries, no two in the same row or column, which are pairwise distinct. A longstanding conjecture of Ryser states that every Latin square with odd order has a latin transversal. Some results on the existence of a large partial latin transversal can be found in [11,6,16]. Mainly motivated by Ryser’s conjecture, Erdős and Spencer [8] p...

A detailed review of the asymptotic matching procedures predicting formation number vortex rings is presented. The original studies Mohseni and Gharib [“A model for universal timescale ring formation,” Phys. Fluids 10(10), 2436–2438 (1998).], Shusser new inviscid rings,” in 30th AIAA Fluid Dynamical Conference (1999).], Linden Turner [“The ‘optimal’ rings, efficiency propulsion devices,” J. Mec...

Let $G=(V,E)$ be a simple connected graph. A perfect matching (or Kekul'e structure in chemical literature) of $G$ is a set of disjoint edges which covers all vertices of $G$. The anti-forcing number of $G$ is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching and is denoted by $af(G)$. In this paper we consider some specifi...

For a k-graph F?[n]k, the clique number of F is defined to be maximum size subset Q [n] with Qk?F. In present paper, we determine edges in on matching at most s and least q for n?8k2s q?(s+1)k?l, n?(s+1)k+s/(3k)?l. Two special cases that q=(s+1)k?2 k=2 are solved completely.