On contractible and vertically contractible elements in 3-connected matroids and graphs
نویسندگان
چکیده
منابع مشابه
On 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...
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...
متن کاملContractible circuits in 3-connected graphs
We show that any 3-cormected graph other than K4 or K5 contains a contractible circuit or contains one of two simple configurations. This leads to a new recursive construction of the 3-connected graphs. (~) 1998 Elsevier Science B.V. All rights reserved
متن کاملOn Hamilton cycles and contractible edges in 3-connected graphs
by R. E. L. Aldred1 University of Otago New Zealand
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00385-8