Rainbow -factors.
Connected odd dominating sets in graphs
An odd dominating set of a simple, undirected graph G = (V,E) is a set of vertices D ⊆ V such that |N[v] ∩ D| ≡ 1 mod 2 for all vertices v ∈ V. It is known that every graph has an odd dominating set. In this paper we consider the concept of connected odd dominating sets. We prove that the problem of deciding if a graph has a connected odd dominating set is NP-complete. We also determine the existence or non-existence of such sets in several classes of graphs. Among other results, we prove there...
The order of monochromatic subgraphs with a given minimum degree.
Orthogonal colorings of graphs.
A Turán type problem concerning the powers of the degrees of a graph.
Packing graphs: The packing problem solved.
Efficient covering designs of the complete graph.
A note on the number of edges guaranteeing a in Eulerian bipartite digraphs.
Multigraphs (only) satisfy a weak triangle removal lemma.
Equitable hypergraph orientations.
On the size of dissociated bases.
On rainbow connection.
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