We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
A Twelve Vertex Theorem for 3-Connected Claw-Free Graphs.
- Authors
Chen, Zhi-Hong
- Abstract
The cyclability of a graph H, denoted by C( H), is the largest integer r such that H has a cycle through any r vertices. For a claw-free graph H, by Ryjáček (J Comb Theory Ser B 70:217-224, ) closure concept, there is a $$K_3$$ -free graph G such that the closure $$cl(H)=L(G)$$ . In this note, we prove that for a 3-connected claw-free graph H with its closure $$cl(H)=L(G)$$ , $$C(H)\ge 12$$ if and only if G can not be contracted to the Petersen graph in such a way that each vertex in P is obtained by contracting a nontrivial connected $$K_3$$ -free subgraph. This is an improvement of the main result in Györi and Plummer (Stud Sci Math Hung 38:233-244, ).
- Subjects
GEOMETRIC vertices; MATHEMATICS theorems; MATHEMATICAL connectedness; PETERSEN graphs; INTEGERS; SUBGRAPHS
- Publication
Graphs & Combinatorics, 2016, Vol 32, Issue 2, p553
- ISSN
0911-0119
- Publication type
Article
- DOI
10.1007/s00373-015-1608-4