Let τ(H) be the cover number and ν(H) be the matching number of a hypergraph H. Ryser conjectured that every r-partite hypergraph H satisfies the inequality τ(H) ≤ (r − 1)ν(H). This conjecture is open for all r ≥ 4. For intersecting hypergraphs, namely those with ν(H) = 1, Ryser’s conjecture reduces to τ(H) ≤ r − 1. Even this conjecture is extremely difficult and is open for all r ≥ 6. For infi...

A tournament is an orientation of a complete graph, and in general a multipartite or c-partite tournament is an orientation of a complete c-partite graph. If x is a vertex of a digraph D, then we denote by d(x) and d−(x) the outdegree and the indegree of x, respectively. The global irregularity of a digraph D is de6ned by ig(D) = max{d+(x); d−(x)} − min{d+(y); d−(y)} over all vertices x and y o...

We give sufficient conditions for a tripartite graph to have a spanning subgraph consisting of complete graphs of order 3. This is applied to bound the strong chromatic number of a graph.

We establish almost tight upper and lower approximation bounds for the Vertex Cover problem on dense k-partite hypergraphs.

We introduce a special type of graph embedding called book embedding and apply it to posets. A book embedding scheme for bipartite graphs is given, and is used to extend the embeddings to general k-partite graphs. Finally, we view the Hasse diagram of a poset as a directed k-partite graph and use this scheme to derive a book embedding for arbitrary posets. Using this book embedding scheme, we a...