Triangle packings and 1-factors in oriented graphs
نویسندگان
چکیده
منابع مشابه
Triangle packings and 1-factors in oriented graphs
An oriented graph is a directed graph which can be obtained from a simple undirected graph by orienting its edges. In this paper we show that any oriented graph G on n vertices with minimum indegree and outdegree at least (1/2 − o(1))n contains a packing of cyclic triangles covering all but at most 3 vertices. This almost answers a question of Cuckler and Yuster and is best possible, since for ...
متن کاملTriangle factors in random graphs
A triangle factor of a graph G = (V,E) on n = |V | = 3k vertices, is a subgraph of G consisting of k vertex-disjoint triangles. A result by Krivelevich [9] states that a triangle factor exists in the random graph G(n, p), n = 3k, with probability 1− o(1) if p = Ω(n−2/3+1/15). This was further improved by Jeong Han Kim in [7] to p = ω(n−2/3+1/18). In this paper we improve this to p = n−2/3+o(1)....
متن کاملTriangle Factors in Random Graphs
For a graph G = (V; E) on n vertices, where 3 divides n, a triangle factor is a subgraph of G, consisting of n=3 vertex disjoint triangles (complete graphs on three vertices). We discuss the problem of determining the minimal probability p = p(n), for which a random graph G 2 G(n; p) contains almost surely a triangle factor. This problem (in a more general setting) has been studied by Alon and ...
متن کاملTransitive triangle tilings in oriented graphs
In this paper, we prove an analogue of Corrádi and Hajnal's result. There exists n 0 such that for every n ∈ 3Z when n ≥ n 0 the following holds. If G is an oriented graph on n vertices and δ 0 (G) ≥ 7n/18, then G contains a perfect T T 3-tiling, which is a collection of vertex disjoint transitive triangles covering every vertex of G. This result is best possible, as there exists an oriented gr...
متن کاملOriented colorings of triangle-free planar graphs
Oriented graphs are directed graphs without opposite arcs. In other words an oriented graph is an orientation of an undirected graph, obtained by assigning to every edge one of the two possible orientations. IfG is a graph, V (G) denotes its vertex set, E(G) denotes its set of edges (or arcs if G is an oriented graph) and F (G) denotes its set of faces if G is planar. A homomorphism from an ori...
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: Journal of Combinatorial Theory, Series B
سال: 2009
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2008.12.004