منابع مشابه
Contractible bonds in graphs
This paper addresses a problem posed by Oxley (Matroid Theory, Cambridge University Press, Cambridge, 1992) for matroids.We shall show that ifG is a 2-connected graph which is not a multiple edge, and which has no K5-minor, then G has two edge-disjoint non-trivial bonds B for which G/B is 2-connected. © 2004 Elsevier Inc. All rights reserved. MSC: 05C38; 05C40; 05C70
متن کاملContractible Subgraphs in 3-Connected Graphs
For a graph G we define a graph T (G) whose vertices are the triangles in G and two vertices of T (G) are adjacent if their corresponding triangles in G share an edge. Kawarabayashi showed that if G is a k-connected graph and T (G) contains no edge then G admits a kcontractible clique of size at most 3, generalizing an earlier result of Thomassen. In this paper, we further generalize Kawarabaya...
متن کاملContractible edges in 3-connected graphs
By a graph, we mean a finite undirected simple graph with no loops and no multiple edges. For a graph G and an edge e of G, we let G/e denote the graph obtained from G by contracting e (and replacing each pair of the resulting double edges by a simple edge). Let k ≥ 2 be an integer, and let G be a k-connected graph. An edge e of G is said to be k-contractible if G/e is k-connected. The set of k...
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The existence of contractible edges is a very useful tool in graph theory. For 3-connected graphs with at least six vertices, Ota and Saito (1988) prove that the set of contractible edges cannot be covered by two vertices. Saito (1990) prove that if a three-element vertex set S covers all contractible edges of a 3-connected graph G, then S is a vertex-cut of G provided that G has at least eight...
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: Journal of Combinatorial Theory, Series B
سال: 2005
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2004.10.002