Corpus ID: 236469515

On fractional version of oriented coloring

@article{Das2021OnFV,
  title={On fractional version of oriented coloring},
  author={Sandip Das and Soham Das and S. Prabhu and Sagnik Sen},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.13443}
}
  • Sandip Das, Soham Das, +1 author Sagnik Sen
  • Published 2021
  • Computer Science, Mathematics
  • ArXiv
We introduce the fractional version of oriented coloring and initiate its study. We prove some basic results and study the parameter for directed cycles and sparse planar graphs. In particular, we show that for every ǫ > 0, there exists an integer gǫ ≥ 12 such that any oriented planar graph having girth at least gǫ has fractional oriented chromatic number at most 4+ ǫ. Whereas, it is known that there exists an oriented planar graph having girth at least gǫ with oriented chromatic number equal… Expand

Figures from this paper

References

SHOWING 1-7 OF 7 REFERENCES
Outerplanar and Planar Oriented Cliques
TLDR
It is proved that an outerplanar graph can be oriented as an oriented clique if and only if it contains one of these graphs as a spanning subgraph, thus reproving the above conjecture. Expand
Homomorphisms and colourings of oriented graphs: An updated survey
  • É. Sopena
  • Computer Science, Mathematics
  • Discret. Math.
  • 2016
TLDR
The main results about oriented colourings are surveyed and a few open problems are proposed and a new oriented chromatic number is proposed. Expand
Good and Semi-Strong Colorings of Oriented Planar Graphs
TLDR
It is shown that every oriented planar graph G = (V,A) with d-(x) ⩽ 3 for every x ϵ V has a good and semi-strong coloring using at most 4 x 5 x 24 colors. Expand
On nice graphs
TLDR
The structure of nice digraphs and multigraphs is studied and it is shown that for every two vertices x and y in G and every pattern of length k , given as a sequence of pluses and minuses, there exists a walk of length x to y which respects this pattern. Expand
Fractional Graph Theory: A Rational Approach to the Theory of Graphs
General Theory: Hypergraphs. Fractional Matching. Fractional Coloring. Fractional Edge Coloring. Fractional Arboricity and Matroid Methods. Fractional Isomorphism. Fractional Odds and Ends. Appendix.Expand
The Monadic Second order Logic of Graphs VI: on Several Representations of Graphs By Relational Structures
  • B. Courcelle
  • Mathematics, Computer Science
  • Discret. Appl. Math.
  • 1994
Abstract The same properties of graphs of degree at most k, where k is a fixed integer, can be expressed by monadic second-order formulas using edge and vertex quantifications as well as by monadicExpand
Find out the fractional oriented chromatic numbers of all the families of oriented planar graphs having girth at least g