On the Pósa-Seymour conjecture
نویسندگان
چکیده
Paul Seymour conjectured that any graph G of order n and minimum degree at least k k+1n contains the k th power of a Hamilton cycle. We prove the following approximate version. For any > 0 and positive integer k, there is an n0 such that, if G has order n ≥ n0 and minimum degree at least ( k k+1 + )n, then G contains the kth power of a Hamilton cycle. c © 1998 John Wiley & Sons, Inc. J Graph Theory
منابع مشابه
The Erdos-Posa Property for Directed Graphs
A classical result by Erdős and Pósa[3] states that there is a function f : N → N such that for every k, every graph G contains k pairwise vertex disjoint cycles or a set T of at most f(k) vertices such that G− T is acyclic. The generalisation of this result to directed graphs is known as Younger’s conjecture and was proved by Reed, Robertson, Seymour and Thomas in 1996. This so-called Erdős-Pó...
متن کاملRobustness of Pósa’s conjecture Master Thesis
The kth power of a cycle is obtained by adding an edge between all pairs of vertices whose distance on the cycle is at most k. In 1962, Pósa conjectured that a graph G on n vertices contains a square of a Hamilton cycle if it has minimum degree δ(G) ≥ 3 n, and, 11 years later, Seymour claimed that δ(G) ≥ k k+1 n is sufficient for the appearance of a kth power of a Hamilton cycle for any k ≥ 2. ...
متن کاملExcluded Forest Minors and the Erdős-Pósa Property
A classical result of Robertson and Seymour states that the set of graphs containing a fixed planar graph H as a minor has the so-called Erdős–Pósa property; namely, there exists a function f depending only on H such that, for every graph G and every positive integer k, the graph G has k vertex-disjoint subgraphs each containing H as a minor, or there exists a subset X of vertices of G with |X|...
متن کاملPacking Topological Minors Half-Integrally
A family F of graphs has the Erdős-Pósa property if for every graph G, the maximum number of pairwise disjoint subgraphs isomorphic to members of F contained in G and the minimum size of a set of vertices of G hitting all such subgraphs are bounded by functions of each other. Robertson and Seymour proved that if F consists of H-minors for some fixed graph H, then the planarity of H is equivalen...
متن کاملHow to avoid using the Regularity Lemma: Pósa's conjecture revisited
In this paper we investigate how the use of the Regularity Lemma and the Blow-up Lemma can be avoided in certain extremal problems of dense graphs. We present the ideas for the following well-known Pósa conjecture on the square of a Hamiltonian cycle. In 1962 Pósa conjectured that any graph G of order n and minimum degree at least 3n contains the square of a Hamiltonian cycle. In an earlier pap...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 29 شماره
صفحات -
تاریخ انتشار 1998