منابع مشابه
Generating 4-connected graphs
5 Let C = {C n : n ≥ 5} and let L = {G : G is the line graph of an internally 4-connected cubic graph}. 6 A classical result of Martinov states that every 4-connected graph G can be constructed from graphs in 7 C ∪L by repeatedly splitting vertices. In this paper we prove that, in fact, G can be constructed from C 5 8 or C 6 in the same way, unless G belongs to C ∪L. Moreover, if G is nonplanar...
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Let c (k) (c. (k» be the least number of vertices of a planar (planar connected) graph whose automorphism group is the cyclic group of order k. If k r is odd and if k = PIal. . . p,ar, PI' . . . ,Pr being primes then c (k) = 3 2: Piai and i=l c. (k) ~ c (k) for r ~ 1 while c. (k) = c (k) + 1 for r> 1. It is conjectured that a similar result holds for k even.
متن کامل4-connected Projective-planar Graphs Are Hamiltonian-connected
We generalize the following two seminal results. 1. Thomassen’s result [19] in 1983, which says thatevery 4-connected planar graph is hamiltonian-connected (which generalizes the old result of Tutte[20] in 1956, which says that every 4-connectedplanar graph is hamiltonian). 2. Thomas and Yu’s result [16] in 1994, which saysthat every 4-connected projective planar graph is<lb...
متن کاملCycles 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 کاملUnavoidable parallel minors of 4-connected graphs
A parallel minor is obtained from a graph by any sequence of edge contractions and parallel edge deletions. We prove that, for any positive integer k, every internally 4-connected graph of sufficiently high order contains a parallel minor isomorphic to a variation of K4,k with a complete graph on the vertices of degree k, the k-partition triple fan with a complete graph on the vertices of degre...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1984
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1984-0743738-4