On a perfect matching in a random digraph with average out-degree below two

On perfect matchings in random bipartite graphs with minimum degree at least two

Perfect matching in 3 uniform hypergraphs with large vertex degree

A perfect matching in a 3-uniform hypergraph on n = 3k vertices is a subset of n3 disjoint edges. We prove that if H is a 3-uniform hypergraph on n = 3k vertices such that every vertex belongs to at least ( n−1 2 ) − ( 2n/3 2 ) + 1 edges then H contains a perfect matching. We give a construction to show that this result is best possible.

In-degree sequence in a general model of a random digraph

A general model of a random digraph D(n,P) is considered. Based on a precise estimate of the asymptotic behaviour of the distribution function of the binomial law, a problem of the distribution of extreme in-degrees of D(n,P) is discussed.

two-out degree equitable domination in graphs

an equitable domination has interesting application in the contextof social networks. in a network, nodes with nearly equal capacitymay interact with each other in a better way. in the societypersons with nearly equal status, tend to be friendly. in thispaper, we introduce new variant of equitable domination of agraph. basic properties and some interesting results have beenobtained.

Blocks in Constrained Random Graphs with Fixed Average Degree

This work is devoted to the study of typical properties of random graphs from classes with structural constraints, like for example planar graphs, with the additional restriction that the average degree is fixed. More precisely, within a general analytic framework, we provide sharp concentration results for the number of blocks (maximal biconnected subgraphs) in a random graph from the class in...