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- Title
On Superconnectivity of (4, g)-Cages.
- Authors
Lu, Hongliang; Wu, Yunjian; Lin, Yuqing; Yu, Qinglin; Balbuena, Camino; Marcote, Xavier
- Abstract
A ( k, g)- cage is a graph that has the least number of vertices among all k-regular graphs with girth g. It has been conjectured (Fu et al. in J. Graph Theory, 24:187-191, ) that all ( k, g)-cages are k-connected for every k ≥ 3. A k-connected graph G is called superconnected if every k-cutset S is the neighborhood of some vertex. Moreover, if G− S has precisely two components, then G is called tightly superconnected. In this paper, we prove that every (4, g)-cage is tightly superconnected when g ≥ 11 is odd.
- Subjects
GRAPH connectivity; REGULAR graphs; MATHEMATICAL proofs; GRAPH theory; MATHEMATICAL analysis
- Publication
Graphs & Combinatorics, 2013, Vol 29, Issue 1, p105
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-011-1091-5