Minimum H-decompositions of graphs: Edge-critical case
نویسندگان
چکیده
For a given graph H let φH (n) be the maximum number of parts that are needed to partition the edge set of any graph on n vertices such that every member of the partition is either a single edge or it is isomorphic to H. Pikhurko and Sousa conjectured that φH (n) = ex(n,H) for χ(H) ≥ 3 and all sufficiently large n, where ex(n,H) denotes the maximum size of a graph on n vertices not containing H as a subgraph. In this article, their conjecture is verified for all edge-critical graphs. Furthermore, it is shown that the graphs maximizing φH(n) are (χ(H) − 1)-partite Turán graphs.
منابع مشابه
H-Decompositions of r-graphs when H is an r-graph with exactly 2 edges
Given two r-graphs G and H, an H-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms a graph isomorphic to H. The minimum number of parts in an H-decomposition of G is denoted by φH(G). By a 2-edge-decomposition of an r-graph we mean an H-decomposition for any fixed r-graph H with exactly 2 edges. In the special case where the two edges of...
متن کاملMinimum rainbow H-decompositions of graphs
Given graphs G and H, we consider the problem of decomposing a properly edge-colored graph G into few parts consisting of rainbow copies of H and single edges. We establish a close relation to the previously studied problem of minimum H-decompositions, where an edge coloring does not matter and one is merely interested in decomposing graphs into copies of H and single edges.
متن کاملMinimum Weight H-Decompositions of Graphs: The Bipartite Case
Given graphs G and H and a positive number b, a weighted (H, b)-decomposition of G is a partition of the edge set of G such that each part is either a single edge or forms an H-subgraph. We assign a weight of b to each H-subgraph in the decomposition and a weight of 1 to single edges. The total weight of the decomposition is the sum of the weights of all elements in the decomposition. Let φ(n,H...
متن کاملOn Total Edge Irregularity Strength of Staircase Graphs and Related Graphs
Let G=(V(G),E(G)) be a connected simple undirected graph with non empty vertex set V(G) and edge set E(G). For a positive integer k, by an edge irregular total k-labeling we mean a function f : V(G)UE(G) --> {1,2,...,k} such that for each two edges ab and cd, it follows that f(a)+f(ab)+f(b) is different from f(c)+f(cd)+f(d), i.e. every two edges have distinct weights. The minimum k for which G ...
متن کاملChromatically Supremal Decompositions of Graphs
If G is a graph, a G-decomposition of a host graph H is a partition of the edges of H into subgraphs of H which are isomorphic to G. The chromatic index of a Gdecomposition of H is the minimum number of colors required to color the parts of the decomposition so that parts which share a common node get different colors. We establish an upper bound on the chromatic index and characterize those de...
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:
- J. Comb. Theory, Ser. B
دوره 102 شماره
صفحات -
تاریخ انتشار 2012