The Strong Perfect Graph Conjecture of Claude Berge is now nearly 25 years old. Efforts to resolve the conjecture almost always use an approach which is quot;graphicalquot; in spirit. A proof by Lobb threw open the interesting possibility that the hypergraph, instead of the graph, could be employed to resolve the conjecture. Here, we study Lobb's theorem in some detail, propose a simpler proof, but end up discovering that this approach can at best help verify the strong conjecture for special classes of graphs. The winning proof is, probably, still very far away
A graph G is perfect if for every induced subgraph F of G, the chromatic number χ(F) equals the larg...
A graph is Berge if no induced subgraph of G is an odd cycle of length at least five or the compleme...
Several classes of hypergraphs have been defined, or characterised, in terms of cycles. Such a formu...
The Strong Perfect Graph Conjecture of Claude Berge is now nearly 25 years old. Efforts to resolve t...
In 1961, Claude Berge proposed the \strong perfect graph conjecture", probably the most beautif...
In 1961, Claude Berge proposed the “strong perfect graph conjecture”, probably the most beautiful op...
Perfect graphs were defined by Claude Berge in the 1960s. They are important objects for graph theor...
AbstractPerfect Graphs were defined by Claude Berge in 1961. Since that time this class of graphs ha...
International audienceThe Strong Perfect Graph Conjecture (SPGC) was certainly one of the most chall...
AbstractA graph G is perfect if for every induced subgraph F of G, the chromatic number χ(F) equals ...
Robertson, Seymour and Thomas in a paper of 146 pages long (see [1]); in this manuscript, via an ori...
AbstractPartitionable graphs have been studied by a number of authors in conjunction with attempts a...
AbstractIn this paper we prove the validity of the Strong Perfect Graph Conjecture for some classes ...
AbstractThe Strong Perfect Graph Conjecture (SPGC) was certainly one of the most challenging conject...
A graph is Berge if no induced subgraph of G is an odd cycle of length at least five or the compleme...
A graph G is perfect if for every induced subgraph F of G, the chromatic number χ(F) equals the larg...
A graph is Berge if no induced subgraph of G is an odd cycle of length at least five or the compleme...
Several classes of hypergraphs have been defined, or characterised, in terms of cycles. Such a formu...
The Strong Perfect Graph Conjecture of Claude Berge is now nearly 25 years old. Efforts to resolve t...
In 1961, Claude Berge proposed the \strong perfect graph conjecture", probably the most beautif...
In 1961, Claude Berge proposed the “strong perfect graph conjecture”, probably the most beautiful op...
Perfect graphs were defined by Claude Berge in the 1960s. They are important objects for graph theor...
AbstractPerfect Graphs were defined by Claude Berge in 1961. Since that time this class of graphs ha...
International audienceThe Strong Perfect Graph Conjecture (SPGC) was certainly one of the most chall...
AbstractA graph G is perfect if for every induced subgraph F of G, the chromatic number χ(F) equals ...
Robertson, Seymour and Thomas in a paper of 146 pages long (see [1]); in this manuscript, via an ori...
AbstractPartitionable graphs have been studied by a number of authors in conjunction with attempts a...
AbstractIn this paper we prove the validity of the Strong Perfect Graph Conjecture for some classes ...
AbstractThe Strong Perfect Graph Conjecture (SPGC) was certainly one of the most challenging conject...
A graph is Berge if no induced subgraph of G is an odd cycle of length at least five or the compleme...
A graph G is perfect if for every induced subgraph F of G, the chromatic number χ(F) equals the larg...
A graph is Berge if no induced subgraph of G is an odd cycle of length at least five or the compleme...
Several classes of hypergraphs have been defined, or characterised, in terms of cycles. Such a formu...