Distribution of contractible edges in k-connected graphs
نویسندگان
چکیده
منابع مشابه
Contractible 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...
متن کاملNote on k-contractible edges in k-connected graphs
It is proved that if G is a k-connected graph which does not contain K;; with k being odd, then G has an edge e such that the graph obtained from G by contracting e is still k-connected. The same conclusion does not hold when k is even. This result is a generalization of the famous theorem of Thomassen [J. Graph Theory 5 (1981), 351--354] when k is odd.
متن کاملContractible Edges and Triangles in k-Connected Graphs
It is proved that if G is a k-connected graph which does not contain K 4 , then G has an edge e or a triangle T such that the graph obtained from G by connecting e or by contracting T is still k-connected. By using this theorem, we prove some theorems which are generalizations of earlier work. In addition, we give a condition for a k-connected graph to have a k-contractible edge, which implies ...
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...
متن کاملOn contractible edges in 3-connected graphs
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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1990
ISSN: 0095-8956
DOI: 10.1016/0095-8956(90)90126-k