Spectral radius and clique partitions of graphs

Clique Partitions of Glued Graphs

A glued graph at K2-clone (K3-clone) results from combining two vertex-disjoint graphs by identifying an edge (a triangle) of each original graph. The clique covering numbers of these desired glued graphs have been investigated recently. Analogously, we obtain bounds of the clique partition numbers of glued graphs at K2-clones and K3-clones in terms of the clique partition numbers of their orig...

Clique Partitions of Dense Graphs

In this paper, we prove that for any forest F ⊂ Kn, the edges of E(Kn)\E(F ) can be partitioned into O(n log n) cliques. This extends earlier results on clique partitions of the complement of a perfect matching and of a hamiltonian path in Kn. We also show that if a graph G has maximum degree 4, then the edges of E(Kn)\E(G) can be partitioned into roughly n 3 24 1 2 log n cliques provided there...

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...

Clique partitions and clique coverings

Several new tools are presented for determining the number of cliques needed to (edge-)partition a graph . For a graph on n vertices, the clique partition number can grow cn z times as fast as the clique covering number, where c is at least 1/64. If in a clique on n vertices, the edges between en° vertices are deleted, Z--a < 1, then the number of cliques needed to partition what is left is asy...

Spectral radius of bipartite graphs