A k−clique covering of a simple graph G, is an edge covering of G by its cliques such that each vertex is contained in at most k cliques. The smallest k for which G admits a k−clique covering is called local clique cover number of G and is denoted by lcc(G). Local clique cover number can be viewed as the local counterpart of the clique cover number which is equal to the minimum total number of cliques covering all edges. In this paper, several aspects of the problem are studied and its relationships to other well-known problems are discussed. Moreover, the local clique cover number of claw-free graphs and its subclasses are notably investigated. In particular, it is proved that local clique cover number of every claw-free graph is at most c...
AbstractWe prove that a locally cobipartite graph on n vertices contains a family of at most n cliqu...
AbstractA biclique B of a simple graph G is the edge-set of a complete bipartite subgraph of G. A bi...
The edges of the random graph (with the edge probability p=1/2) can be covered using O(n 2 lnln n/(l...
An edge clique cover of a graph is a set of cliques that covers all edges of the graph. We generaliz...
AbstractConsider a graph G with the property that any set of p vertices in G contains a q-clique. Fa...
AbstractConsider a graph G with the property that any set of p vertices in G contains a q-clique. Fa...
AbstractA clique in a graph G is a complete subgraph of G. A clique covering (partition) of G is a c...
A clique covering of a graph G is a set of cliques of G such that any edge of G is contained in one ...
AbstractWe prove that a locally cobipartite graph on n vertices contains a family of at most n cliqu...
International audienceWe consider the problem of covering an input graph H with graphs from a fixed ...
International audienceWe consider the problem of covering an input graph H with graphs from a fixed ...
The problem of covering edges and vertices in a graph (or in a hypergraph) was motivated by a proble...
The problem of covering edges and vertices in a graph (or in a hypergraph) was motivated by a proble...
A biclique B of a simple graph G is the edge-set of a complete bipartite subgraph of G. A biclique c...
A family of cliques in a graph G is said to be p-regular if any two cliques in the family intersect ...
AbstractWe prove that a locally cobipartite graph on n vertices contains a family of at most n cliqu...
AbstractA biclique B of a simple graph G is the edge-set of a complete bipartite subgraph of G. A bi...
The edges of the random graph (with the edge probability p=1/2) can be covered using O(n 2 lnln n/(l...
An edge clique cover of a graph is a set of cliques that covers all edges of the graph. We generaliz...
AbstractConsider a graph G with the property that any set of p vertices in G contains a q-clique. Fa...
AbstractConsider a graph G with the property that any set of p vertices in G contains a q-clique. Fa...
AbstractA clique in a graph G is a complete subgraph of G. A clique covering (partition) of G is a c...
A clique covering of a graph G is a set of cliques of G such that any edge of G is contained in one ...
AbstractWe prove that a locally cobipartite graph on n vertices contains a family of at most n cliqu...
International audienceWe consider the problem of covering an input graph H with graphs from a fixed ...
International audienceWe consider the problem of covering an input graph H with graphs from a fixed ...
The problem of covering edges and vertices in a graph (or in a hypergraph) was motivated by a proble...
The problem of covering edges and vertices in a graph (or in a hypergraph) was motivated by a proble...
A biclique B of a simple graph G is the edge-set of a complete bipartite subgraph of G. A biclique c...
A family of cliques in a graph G is said to be p-regular if any two cliques in the family intersect ...
AbstractWe prove that a locally cobipartite graph on n vertices contains a family of at most n cliqu...
AbstractA biclique B of a simple graph G is the edge-set of a complete bipartite subgraph of G. A bi...
The edges of the random graph (with the edge probability p=1/2) can be covered using O(n 2 lnln n/(l...