منابع مشابه
Cyclic 7-edge-cuts in fullerene graphs
A fullerene graph is a planar cubic graph whose all faces are pentagonal and hexagonal. The structure of cyclic edge-cuts of fullerene graphs of sizes up to 6 is known. In the paper we study cyclic 7-edge connectivity of fullerene graphs, distinguishing between degenerated and non-degenerated cyclic edge-cuts, regarding the arrangement of the 12 pentagons. We prove that if there exists a non-de...
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In an earlier paper [3], we studied cycles in graphs that intersect all edge-cuts of prescribed sizes. Passing to a more general setting, we examine the existence of T -joins in grafts that intersect all edge-cuts whose size is in a given set A ⊆ {1, 2, 3}. In particular, we characterize all the contractionminimal grafts admitting no T -joins that intersect all edge-cuts of size 1 and 2. We als...
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We study graphs G = (V,E) containing a long cycle which for given integers a1, a2, ..., ak ∈ N have an edge cut whose removal results in k components with vertex sets V1, V2, ..., Vk such that |Vi| ≥ ai for 1 ≤ i ≤ k. Our results closely relate to problems and recent research in network sharing and network reliability.
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A 4-restricted edge cut is an edge cut of a connected graph which disconnects the graph, where each component has order at least 4. Graphs that contain 4-restricted edge cuts are characterized in this paper. As a result, it is proved that a connected graph G of order at least 10 contains 4-restricted edge cuts if and only if it contains no cut-vertex u where every component of G \ u has order a...
متن کاملT-joins intersecting small edge-cuts in graphs
In an earlier paper [3], we studied cycles in graphs that intersect all edge-cuts of prescribed sizes. Passing to a more general setting, we examine the existence of T -joins in grafts that intersect all edge-cuts whose size is in a given set A ⊆ {1, 2, 3}. In particular, we characterize all the contractionminimal grafts admitting no T -joins that intersect all edge-cuts of size 1 and 2. We als...
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ژورنال
عنوان ژورنال: Journal of Mathematical Chemistry
سال: 2009
ISSN: 0259-9791,1572-8897
DOI: 10.1007/s10910-009-9599-0