On Rainbow Trees and Cycles
نویسندگان
چکیده
We derive sufficient conditions for the existence of rainbow cycles of all lengths in edge colourings of complete graphs. We also consider rainbow colorings of a certain class of trees.
منابع مشابه
On the outer independent 2-rainbow domination number of Cartesian products of paths and cycles
Let G be a graph. A 2-rainbow dominating function (or 2-RDF) of G is a function f from V(G) to the set of all subsets of the set {1,2} such that for a vertex v ∈ V (G) with f(v) = ∅, thecondition $bigcup_{uin N_{G}(v)}f(u)={1,2}$ is fulfilled, wher NG(v) is the open neighborhoodof v. The weight of 2-RDF f of G is the value$omega (f):=sum _{vin V(G)}|f(v)|$. The 2-rainbowd...
متن کاملEdge 2-rainbow domination number and annihilation number in trees
A edge 2-rainbow dominating function (E2RDF) of a graph G is a function f from the edge set E(G) to the set of all subsets of the set {1,2} such that for any edge.......................
متن کاملRainbow regular order of graphs
Assume that the vertex set of the complete graph Kt is Zt if t is odd and Zt−1 ∪ {∞} otherwise, with convention that x +∞ = 2x. If the color of any edge xy is defined to be x+ y then GKt stands for Kt together with the resulting edge coloring. Hence color classes are maximum matchings rotationally/cyclically generated if t is even/odd. A rainbow subgraph of GKt has all edges with distinct color...
متن کاملAnti-Ramsey Problems for t Edge-Disjoint Rainbow Spanning Subgraphs: Cycles, Matchings, or Trees
We seek the maximum number of colors in an edge-coloring of the complete graph Kn not having t edge-disjoint rainbow spanning subgraphs of specified types. Let c(n, t), m(n, t), and r(n, t) denote the answers when the spanning subgraphs are cycles, matchings, or trees, respectively. We prove c(n, t) = ( 2 ) + t for n ≥ 8t − 1 and m(n, t) = ( 2 ) + t for n > 4t + 10. We prove r(n, t) = ( 2 ) + t...
متن کاملEdge-disjoint rainbow spanning trees in complete graphs
Let G be an edge-colored copy of Kn, where each color appears on at most n/2 edges (the edgecoloring is not necessarily proper). A rainbow spanning tree is a spanning tree of G where each edge has a different color. Brualdi and Hollingsworth [4] conjectured that every properly edge-colored Kn (n ≥ 6 and even) using exactly n−1 colors has n/2 edge-disjoint rainbow spanning trees, and they proved...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Electr. J. Comb.
دوره 15 شماره
صفحات -
تاریخ انتشار 2008