Minimally locally 1-connected graphs
نویسندگان
چکیده
منابع مشابه
Minimally (k, k-1)-edge-connected graphs
For an interger l > 1, the l-edge-connectivity λl(G) of G is defined to be the smallest number of edges whose removal leaves a graph with at least l components, if |V (G)| ≥ l; and λl(G) = |V (G)| if |V (G)| ≤ l. A graph G is (k, l)-edge-connected if the l-edge-connectivity of G is at least k. A sufficient and necessary condition for G to be minimally (k, k − 1)-edgeconnected is obtained in the...
متن کاملCharacterization of minimally (2, l)-connected graphs
For an integer l ≥ 2, the l-connectivity κl(G) of a graph G is defined to be the minimum number of vertices of G whose removal produces a disconnected graph with at least l components or a graph with fewer than l vertices. Let k ≥ 1, a graph G is called (k, l)-connected if κl(G) ≥ k. A graph G is called minimally (k, l)-connected if κl(G) ≥ k but ∀e ∈ E(G), κl(G − e) ≤ k − 1. We present a struc...
متن کاملA note on minimally 3-connected graphs
If G is a minimally 3-connected graph and C is a double cover of the set of edges of G by irreducible walks, then |E (G)| ≥ 2 |C| − 2.
متن کاملNote on minimally k-connected graphs
A k-tree is either a complete graph on (k+1) vertices or given a k-tree G′ with n vertices, a k-tree G with (n+1) vertices can be constructed by introducing a new vertex v and picking a k-clique Q in G′ and then joining each vertex u in Q. A graph G is kedge-connected if the graph remains connected even after deleting fewer edges than k from the graph. A k-edge-connected graph G is said to be m...
متن کاملContractible edges in minimally k-connected graphs
An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. In this paper, we prove that a (K1 + C4)-free minimally k-connected graph has a k-contractible edge, if incident to each vertex of degree k, there is an edge which is not contained in a triangle. This implies two previous results, one due to Thomassen and the other due to K...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1978
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700008467