Displaying similar documents to “Contractible edges in some $k$-connected graphs”

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...

Connected resolving decompositions in graphs

Varaporn Saenpholphat, Ping Zhang (2003)

Mathematica Bohemica

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For an ordered k -decomposition 𝒟 = { G 1 , G 2 , ... , G k } of a connected graph G and an edge e of G , the 𝒟 -code of e is the k -tuple c 𝒟 ( e ) = ( d ( e , G 1 ) , d ( e , G 2 ) , ... , d ( e , G k ) ), where d ( e , G i ) is the distance from e to G i . A decomposition 𝒟 is resolving if every two distinct edges of G have distinct 𝒟 -codes. The minimum k for which G has a resolving k -decomposition is its decomposition dimension dim d ( G ) . A resolving decomposition 𝒟 of G is connected if each G i is connected for 1 i k . The minimum k for which G ...

On connected resolving decompositions in graphs

Varaporn Saenpholphat, Ping Zhang (2004)

Czechoslovak Mathematical Journal

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For an ordered k -decomposition 𝒟 = { G 1 , G 2 , , G k } of a connected graph G and an edge e of G , the 𝒟 -code of e is the k -tuple c 𝒟 ( e ) = ( d ( e , G 1 ) , d ( e , G 2 ) , ... , d ( e , G k ) ) , where d ( e , G i ) is the distance from e to G i . A decomposition 𝒟 is resolving if every two distinct edges of G have distinct 𝒟 -codes. The minimum k for which G has a resolving k -decomposition is its decomposition dimension dim d ( G ) . A resolving decomposition 𝒟 of G is connected if each G i is connected for 1 i k . The minimum k for which G has a connected resolving k -decomposition is its connected decomposition...