Equitable partitions into matchings and coverings in mixed graphs

Partitions of Graphs into Coverings and Hypergraphs into Transversals

A covering of a multigraph G is a subset of edges which meet ail vertices of G. Partitions of the edges of G into coverings Ci, C2,..., Ck are considered. In particular we examine how close the cardinalities of thèse coverings may be. A resuit concerning matchings is extended to the décomposition into coverings. Finally thèse considérations are generalized to the décompositions of the vertices ...

Coverings, matchings and paired domination in fuzzy graphs using strong arcs

The concepts of covering and matching in fuzzy graphs using strong arcs are introduced and obtained the relationship between them analogous to Gallai’s results in graphs. The notion of paired domination in fuzzy graphs using strong arcs is also studied. The strong paired domination number γspr of complete fuzzy graph and complete bipartite fuzzy graph is determined and obtained bounds for the s...

Clique coverings and partitions of line graphs

A clique in a graph G is a complete subgraph of G. A clique covering (partition) of G is a collection C of cliques such that each edge of G occurs in at least (exactly) one clique in C. The clique covering (partition) number cc(G) (cp(G)) of G is the minimum size of a clique covering (partition) of G. This paper gives alternative proofs, using a unified approach, for the results on the clique c...

Equitable Partitions and Orbit Partitions

We consider two kinds of partition of a graph, namely orbit partitions and equitable partitions. Although an orbit partition is always an equitable partition, the converse is not true in general. We look at some classes of graphs for which the converse is true.

I. Matchings and coverings