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.
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Finding edge-disjoint odd cycles is one of the most important problems in graph theory, graph algorithm and combinatorial optimization. In fact, it is closely related to the well-known max-cut problem. One of the difficulties of this problem is that the Erdős-Pósa property does not hold for odd cycles in general. Motivated by this fact, we prove that for any positive integer k, there exists an ...
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A graph G is k-triangular if each edge of G is in at least k triangles. It is conjectured that every 4-edge-connected 1-triangular graph admits a nowhere-zero Z3-flow. However, it has been proved that not all such graphs are Z3-connected. In this paper, we show that every 4-edge-connected 2-triangular graph is Z3-connected. The result is best possible. This result provides evidence to support t...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90170-8