A Dirac-Type Result on Hamilton Cycles in Oriented Graphs
نویسندگان
چکیده
منابع مشابه
A Dirac-Type Result on Hamilton Cycles in Oriented Graphs
We show that for each α > 0 every sufficiently large oriented graph G with δ(G), δ−(G) ≥ 3|G|/8 + α|G| contains a Hamilton cycle. This gives an approximate solution to a problem of Thomassen [21]. In fact, we prove the stronger result that G is still Hamiltonian if δ(G) + δ(G) + δ−(G) ≥ 3|G|/2 + α|G|. Up to the term α|G| this confirms a conjecture of Häggkvist [10]. We also prove an Ore-type th...
متن کاملCompatible Hamilton cycles in Dirac graphs
A graph is Hamiltonian if it contains a cycle passing through every vertex exactly once. A celebrated theorem of Dirac from 1952 asserts that every graph on n ≥ 3 vertices with minimum degree at least n/2 is Hamiltonian. We refer to such graphs as Dirac graphs. In this paper we obtain the following strengthening of this result. Given a graph G = (V,E), an incompatibility system F over G is a fa...
متن کاملVertex-Oriented Hamilton Cycles in Directed Graphs
Let D be a directed graph of order n. An anti-directed Hamilton cycle H in D is a Hamilton cycle in the graph underlying D such that no pair of consecutive arcs in H form a directed path in D. We prove that if D is a directed graph with even order n and if the indegree and the outdegree of each vertex of D is at least 23n then D contains an anti-directed Hamilton cycle. This improves a bound of...
متن کاملDirac-type results for loose Hamilton cycles in uniform hypergraphs
A classic result of G. A. Dirac in graph theory asserts that every n-vertex graph (n ≥ 3) with minimum degree at least n/2 contains a spanning (so-called Hamilton) cycle. G. Y. Katona and H. A. Kierstead suggested a possible extension of this result for k-uniform hypergraphs. There a Hamilton cycle of an n-vertex hypergraph corresponds to an ordering of the vertices such that every k consecutiv...
متن کاملArbitrary Orientations of Hamilton Cycles in Oriented Graphs
We use a randomised embedding method to prove that for all α > 0 any sufficiently large oriented graph G with minimum in-degree and outdegree δ+(G), δ−(G) ≥ (3/8+α)|G| contains every possible orientation of a Hamilton cycle. This confirms a conjecture of Häggkvist and Thomason.
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: Combinatorics, Probability and Computing
سال: 2008
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548308009218