Long cycles in subgraphs of (pseudo)random directed graphs

Hamilton cycles in random subgraphs of pseudo-random graphs

Distribution of certain sparse spanning subgraphs in random graphs

We describe a general approach of determining the distribution of spanning subgraphs in the random graph G(n, p). In particular, we determine the distribution of spanning subgraphs of certain given degree sequences, which is a generalisation of the d-factors, of spanning trianglefree subgraphs, of (directed) Hamilton cycles and of spanning subgraphs that are isomorphic to a collection of vertex...

The Regularity Lemma of Szemerédi for Sparse Graphs

In this note we present a new version of the well-known lemma of Szemerédi [17] concerning regular partitions of graphs. Our result deals with subgraphs of pseudo-random graphs, and hence may be used to partition sparse graphs that do no contain dense subgraphs.

Hamilton Cy les in Random Subgraphs of Pseudo-Random Graphs

Independent domination in directed graphs

In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...