Colorings of infinite graphs without one-colored rays
β Scribed by Norbert Polat
- Book ID
- 102648176
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 773 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
The R-chromatic number of a graph G is the least number of subsets of vertices forming a partition of V ( G ) , and which induce subgraphs of G without infinite paths. For any integer n 2 2, we give sufficient conditions for a graph containing no subdivision of an infinite complete graph to have a R-chromatic number 5 n. 0
π SIMILAR VOLUMES
## Abstract It is well known that every planar graph __G__ is 2βcolorable in such a way that no 3βcycle of __G__ is monochromatic. In this paper, we prove that __G__ has a 2βcoloring such that no cycle of length 3 or 4 is monochromatic. The complete graph __K__~5~ does not admit such a coloring. On
It is shown that there is a constant \(c\) such that if \(G\) is a graph embedded in a surface of genus \(g\) (either orientable or non-orientable) and the length of a shortest non-bounding cycle of \(G\) is at least \(c \log (g+1)\), then \(G\) is six-colorable. A similar result holds for three- an