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Displaying similar documents to “Two operations on a graph preserving the (non)existence of 2-factors in its line graph”

The contractible subgraph of 5 -connected graphs

Chengfu Qin, Xiaofeng Guo, Weihua Yang (2013)

Czechoslovak Mathematical Journal

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An edge e of a k -connected graph G is said to be k -removable if G - e is still k -connected. A subgraph H of a k -connected graph is said to be k -contractible if its contraction results still in a k -connected graph. A k -connected graph with neither removable edge nor contractible subgraph is said to be minor minimally k -connected. In this paper, we show that there is a contractible subgraph in a 5 -connected graph which contains a vertex who is not contained in any triangles. Hence, every vertex...

The eavesdropping number of a graph

Jeffrey L. Stuart (2009)

Czechoslovak Mathematical Journal

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Let G be a connected, undirected graph without loops and without multiple edges. For a pair of distinct vertices u and v , a minimum { u , v } -separating set is a smallest set of edges in G whose removal disconnects u and v . The edge connectivity of G , denoted λ ( G ) , is defined to be the minimum cardinality of a minimum { u , v } -separating set as u and v range over all pairs of distinct vertices in G . We introduce and investigate the eavesdropping number, denoted ε ( G ) , which is defined to be the maximum cardinality...

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...