Vertex colorings with a distance restriction
نویسندگان
چکیده
منابع مشابه
Vertex colorings with a distance restriction
Let d, k be any two positive integers with k > d > 0. We consider a k-coloring of a graph G such that the distance between each pair of vertices in the same color-class is at least d. Such graphs are said to be (k,d)-colorable. The object of this paper is to determine the maximum size of (k, 3)-colorable, (k, 4)-colorable, and (k, k 1 )-colorable graphs. Sharp results are obtained for both (k, ...
متن کاملVertex rainbow colorings of graphs
In a properly vertex-colored graphG, a path P is a rainbow path if no two vertices of P have the same color, except possibly the two end-vertices of P . If every two vertices of G are connected by a rainbow path, then G is vertex rainbow-connected. A proper vertex coloring of a connected graph G that results in a vertex rainbow-connected graph is a vertex rainbow coloring ofG. The minimum numbe...
متن کاملAdjacent Vertex Distinguishing Edge-Colorings
An adjacent vertex distinguishing edge-coloring of a simple graph G is a proper edge-coloring of G such that no pair of adjacent vertices meets the same set of colors. The minimum number of colors χa(G) required to give G an adjacent vertex distinguishing coloring is studied for graphs with no isolated edge. We prove χa(G) ≤ 5 for such graphs with maximum degree Δ(G) = 3 and prove χa(G) ≤ Δ(G) ...
متن کاملA note on acyclic vertex-colorings
We prove that the acyclic chromatic number of a graph with maximum degree ∆ is less than 2.835∆4/3+∆. This improves the previous upper bound, which was 50∆4/3. To do so, we draw inspiration from works by Alon, McDiarmid and Reed and by Esperet and Parreau.
متن کاملVertex colorings without rainbow subgraphs
Given a coloring of the vertices of a graph G, we say a subgraph is rainbow if its vertices receive distinct colors. For graph F , we define the F -upper chromatic number of G as the maximum number of colors that can be used to color the vertices of G such that there is no rainbow copy of F . We present some results on this parameter for certain graph classes. The focus is on the case that F 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
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00094-6