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...
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Let D = (V,E) be a minimally k-edge-connected simple directed graph. We prove that there is a function f(k) such that |V | ≥ f(k) implies |E| ≤ 2k(|V | − k). We also determine the extremal graphs whose size attains this upper bound.
متن کاملOn minimally rainbow k-connected graphs
An edge-coloured graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colours. A graph G is called rainbow k-connected, if there is an edge-colouring of G with k colours such that G is rainbow-connected. In this talk we will study rainbow k-connected graphs with a minimum number of edges. For an integer n ≥ 3 and 1 ≤ k ≤ n − 1 let t(n, k) denote the...
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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 کاملOn critically k-edge-connected graphs
Let G be a simple graph on n vertices having edge-connectivity /(.' (G) > a and minimum degree o(G) We say G is k-critical if /(.' (G) = k and /(.' (G e) < k for every edge e of G. In this paper we prove that a k-critical graph has 1<' (G) o(G). We descri be a number of classes of k-cri tical graphs and consider the problem of determining the edge-maximal ones.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1978
ISSN: 0012-365X
DOI: 10.1016/0012-365x(78)90198-x