منابع مشابه
Contractible Cliques in k-Connected Graphs
Kawarabayashi proved that for any integer k ≥ 4, every k-connected graph contains two triangles sharing an edge, or admits a k-contractible edge, or admits a k-contractible triangle. This implies Thomassen’s result that every triangle-free k-connected graph contains a k-contractible edge. In this paper, we extend Kawarabayashi’s technique and prove a more general result concerning k-contractibl...
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...
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 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...
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 2006
ISSN: 0911-0119,1435-5914
DOI: 10.1007/s00373-006-0670-3