Colorings Of Plane Graphs With No Rainbow Faces
نویسندگان
چکیده
منابع مشابه
Non-rainbow colorings of 3-, 4- and 5-connected plane graphs
We study vertex-colorings of plane graphs that do not contain a rainbow face, i.e., a face with vertices of mutually distinct colors. If G is 3-connected plane graph with n vertices, then the number of colors in such a coloring does not exceed ⌊ 7n−8 9 ⌋ . If G is 4-connected, then the number of colors is at most ⌊ 5n−6 8 ⌋ , and for n ≡ 3 (mod 8), it is at most ⌊ 5n−6 8 ⌋ − 1. Finally, if G is...
متن کاملComplete Bipartite Graphs with No Rainbow Paths
Motivated by questions in Ramsey theory, Thomason and Wagner described the edge colorings of complete graphs that contain no rainbow path Pt of order t. In this paper, we consider the edge colorings of complete bipartite graphs that contain no rainbow path Pt. Mathematics Subject Classification: 05C15, 05C38, 05C55
متن کاملDisconnected Colors in Generalized Gallai-Colorings
Gallai-colorings of complete graphs—edge colorings such that no triangle is colored with three distinct colors—occur in various contexts such as the theory of partially ordered sets (in Gallai’s original paper), information theory and the theory of perfect graphs. A basic property of GallaiQ1 colorings with at least three colors is that at least one of the color classes must span a disconnected...
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 کاملRainbow faces in edge-colored plane graphs
A face of an edge colored plane graph is called rainbow if all its edges receive distinct colors. The maximum number of colors used in an edge coloring of a connected plane graph G with no rainbow face is called the edge-rainbowness of G. In this paper we prove that the edge-rainbowness of G equals to the maximum number of edges of a connected bridge face factor H of G, where a bridge face fact...
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:
- Combinatorica
دوره 26 شماره
صفحات -
تاریخ انتشار 2006