The minimum degree threshold for perfect graph packings
نویسندگان
چکیده
Let H be any graph. We determine (up to an additive constant) the minimum degree of a graph G which ensures that G has a perfect H-packing. More precisely, let δ(H, n) denote the smallest integer k such that every graph G whose order n is divisible by |H| and with δ(G) ≥ k contains a perfect H-packing. We show that
منابع مشابه
On Perfect Packings in Dense Graphs
We say that a graph G has a perfect H-packing if there exists a set of vertex-disjoint copies of H which cover all the vertices in G. We consider various problems concerning perfect Hpackings: Given n, r,D ∈ N, we characterise the edge density threshold that ensures a perfect Kr-packing in any graph G on n vertices and with minimum degree δ(G) ≥ D. We also give two conjectures concerning degree...
متن کاملThe Regularity Lemma and applications to packings in graphs
In this thesis we investigate applications of Szemerédi’s Regularity Lemma [20]. This result was originally formulated to solve number-theoretical problems. However, we consider its applications in graph theory, in particular to packing results. We begin by introducing some of the basic notions that are needed to understand and use the Regularity Lemma. From this we give an outline of some tool...
متن کاملThe Complexity of Perfect Matchings and Packings in Dense Hypergraphs
Given two k-graphs H and F , a perfect F -packing in H is a collection of vertexdisjoint copies of F in H which together cover all the vertices in H. In the case when F is a single edge, a perfect F -packing is simply a perfect matching. For a given fixed F , it is often the case that the decision problem whether an n-vertex k-graph H contains a perfect F -packing is NP-complete. Indeed, if k ≥...
متن کاملA degree sequence Hajnal-Szemerédi theorem
We say that a graph G has a perfect H-packing if there exists a set of vertex-disjoint copies of H which cover all the vertices in G. The seminal Hajnal–Szemerédi theorem [12] characterises the minimum degree that ensures a graph G contains a perfect Kr-packing. Balogh, Kostochka and Treglown [4] proposed a degree sequence version of the Hajnal–Szemerédi theorem which, if true, gives a strength...
متن کاملPerfect packings with complete graphs minus an edge
Let K− r denote the graph obtained from Kr by deleting one edge. We show that for every integer r ≥ 4 there exists an integer n0 = n0(r) such that every graph G whose order n ≥ n0 is divisible by r and whose minimum degree is at least (1−1/χcr(K − r ))n contains a perfect K− r -packing, i.e. a collection of disjoint copies of K− r which covers all vertices of G. Here χcr(K − r ) = r(r−2) r−1 is...
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:
- Combinatorica
دوره 29 شماره
صفحات -
تاریخ انتشار 2009