Monochromatic Kr-Decompositions of Graphs
نویسندگان
چکیده
Given graphs G and H, and a colouring of the edges of G with k colours, a monochromatic 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 monochromatic graph isomorphic to H. Let φk(n,H) be the smallest number φ such that any k-edge-coloured graph G of order n, admits a monochromatic H-decomposition with at most φ parts. Here we study the function φk(n,Kr) for k ≥ 2 and r ≥ 3.
منابع مشابه
Monochromatic Clique Decompositions of Graphs
Let G be a graph whose edges are colored with k colors, and H=(H1,⋯,Hk) be a k-tuple of graphs. A monochromatic 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 monochromatic copy of Hi in color i, for some 1≤i≤k. Let φk(n,H) be the smallest number ϕ, such that, for every order-n graph and every k-edge-coloring, there is a monochrom...
متن کاملMonochromatic KrKr-Decompositions of Graphs
Given graphs G and H, and a colouring of the edges of G with k colours, a monochromatic 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 monochromatic graph isomorphic to H. Let φk(n,H) be the smallest number φ such that any graph G of order n and any colouring of its edges with k colours, admits a monochromatic Hdecomposition with ...
متن کاملMonochromatic K r - Decompositions of Graphs ( Extended Abstract )
Given graphs G and H, and a colouring of the edges of G with k colours, a monochromatic 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 monochromatic graph isomorphic to H. Let φk(n,H) be the smallest number φ such that any k-edge-coloured graph G of order n, admits a monochromatic H-decomposition with at most φ parts. Here we stud...
متن کاملOrthogonal Decomposition and Packing of Complete Graphs
An H-decomposition of a graph G is a partition of the edge-set of G into subsets, where each subset induces a copy of the graph H. A k-orthogonal H-decomposition of a graph G is a set of k H-decompositions of G, such that any two copies of H in distinct H-decompositions intersect in at most one edge. In case G=Kn and H=Kr , a k-orthogonal Kr -decomposition of Kn is called an (n, r, k) completel...
متن کاملThe H-Decomposition Problem for Graphs
The concept of H-decompositions of graphs was first introduced by Erdös, Goodman and Pósa in 1966, who were motivated by the problem of representing graphs by set intersections. Given 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. Let be the smallest number , n H , such that, any g...
متن کامل