Some 4-valent, 3-connected, planar, almost pancyclic graphs
نویسندگان
چکیده
منابع مشابه
Cycles in 4-connected planar graphs
Let G be a 4-connected planar graph on n vertices. Previous results show that G contains a cycle of length k for each k ∈ {n, n − 1, n − 2, n − 3} with k ≥ 3. These results are proved using the “Tutte path” technique, and this technique alone cannot be used to obtain further results in this direction. One approach to obtain further results is to combine Tutte paths and contractible edges. In th...
متن کامل4-Connected Projective-Planar Graphs Are Hamiltonian
We prove the result stated in the title (conjectured by Grünbaum), and a conjecture of Plummer that every graph which can be obtained from a 4–connected planar graph by deleting two vertices is Hamiltonian. The proofs are constructive and give rise to polynomial–time algorithms.
متن کاملNonseparating Planar Chains in 4-Connected Graphs
In this paper, we describe an O(|V (G)|) algorithm for finding a “non-separating planar chain” in a 4-connected graph G, which will be used to decompose an arbitrary 4-connected graph into “planar chains”. This work was motivated by the study of a multi-tree approach to reliability in distributed networks, as well as the study of non-separating induced paths in highly connected graphs. Supporte...
متن کاملInternally 4-connected projective-planar graphs
5 Archdeacon proved that projective-planar graphs are characterized by 35 excluded minors. 6 Using this result we show that internally 4-connected projective-planar graphs are characterized 7 by 23 internally 4-connected excluded minors. 8
متن کاملSome 3-connected 4-edge-critical non-Hamiltonian graphs
Let (G) be the domination number of graph G, thus a graph G is k -edge-critical if (G) 1⁄4 k ; and for every nonadjacent pair of vertices u and v, (Gþ uv) 1⁄4 k 1. In Chapter 16 of the book ‘‘Domination in Graphs— Advanced Topics,’’ D. Sumner cites a conjecture of E. Wojcicka under the form ‘‘3-connected 4-critical graphs are Hamiltonian and perhaps, in general (i.e., for any k 4), (k 1)-connec...
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: 1977
ISSN: 0012-365X
DOI: 10.1016/0012-365x(77)90073-5