Displaying similar documents to “On the connectivity of skeletons of pseudomanifolds with boundary”

The connected forcing connected vertex detour number of a graph

A.P. Santhakumaran, P. Titus (2011)

Discussiones Mathematicae Graph Theory

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For any vertex x in a connected graph G of order p ≥ 2, a set S of vertices of V is an x-detour set of G if each vertex v in G lies on an x-y detour for some element y in S. A connected x-detour set of G is an x-detour set S such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected x-detour set of G is the connected x-detour number of G and is denoted by cdₓ(G). For a minimum connected x-detour set Sₓ of G, a subset T ⊆ Sₓ is called a connected x-forcing...

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...

A Sufficient Condition for Graphs to Be SuperK-Restricted Edge Connected

Shiying Wang, Meiyu Wang, Lei Zhang (2017)

Discussiones Mathematicae Graph Theory

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For a subset S of edges in a connected graph G, S is a k-restricted edge cut if G − S is disconnected and every component of G − S has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is defined as the cardinality of a minimum k-restricted edge cut. Let ξk(G) = min|[X, X̄]| : |X| = k, G[X] is connected, where X̄ = V (G). A graph G is super k-restricted edge connected if every minimum k-restricted edge cut of G isolates a component of order exactly k. Let...

A simple proof of Whitney's Theorem on connectivity in graphs

Kewen Zhao (2011)

Mathematica Bohemica

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In 1932 Whitney showed that a graph G with order n ≥ 3 is 2-connected if and only if any two vertices of G are connected by at least two internally-disjoint paths. The above result and its proof have been used in some Graph Theory books, such as in Bondy and Murty’s well-known Graph Theory with Applications. In this note we give a much simple proof of Whitney’s Theorem.