Displaying similar documents to “A note on the Size-Ramsey number of long subdivisions of graphs”

Cores and shells of graphs

Allan Bickle (2013)

Mathematica Bohemica

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The k -core of a graph G , C k ( G ) , is the maximal induced subgraph H ⊆ G such that δ ( G ) ≥ k , if it exists. For k > 0 , the k -shell of a graph G is the subgraph of G induced by the edges contained in the k -core and not contained in the ( k + 1 ) -core. The core number of a vertex is the largest value for k such that v ∈ C k ( G ) , and the maximum core number of a graph, C ^ ( G ) , is the maximum of the core numbers of the vertices of G . A graph G is k -monocore if C ^ ( G ) = δ ( G ) = k . This paper discusses some basic results on the structure of k -cores and...