Vertex colorings without isolates
نویسندگان
چکیده
منابع مشابه
Vertex 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 کاملVertex Colorings without Rainbow or Monochromatic Subgraphs
This paper investigates vertex colorings of graphs such that some rainbow subgraph R and some monochromatic subgraph M are forbidden. Previous work focussed on the case that R = M . Here we consider the more general case, especially the case that M = K2.
متن کاملVertex colorings of graphs without short odd cycles
Motivated by the work of Nešetřil and Rödl on “Partitions of vertices”, we are interested in obtaining some quantitative extensions of their result. In particular, given a natural number r and a graph G of order m with odd girth g, we show the existence of a graph H with odd girth at least g and order that is polynomial in m such that every r-coloring of the vertices of H yields a monochromatic...
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 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: Journal of Combinatorial Theory, Series B
سال: 1979
ISSN: 0095-8956
DOI: 10.1016/0095-8956(79)90020-0