Figures and Tables from this paper
4 Citations
A Survey on the Cyclic Coloring and its Relaxations
- MathematicsDiscuss. Math. Graph Theory
- 2021
A survey on the state of the art concerning the cyclic coloring and relaxations of this graph invariant.
Facial Rainbow Coloring of Plane Graphs
- MathematicsDiscuss. Math. Graph Theory
- 2019
The facial rainbow number of a plane graph G, denoted by rb(G), is the minimum number of colors that are necessary in any facial rainbow coloring of G.
Square coloring planar graphs with automatic discharging
- Computer Science, MathematicsArXiv
- 2022
This paper uses a Linear Programming approach to automatically look for a discharging proof, and makes some progress towards Wegner’s conjecture for distance- 2 coloring of planar graphs, by showing that 12 colors arecient to color at distance 2 every planar graph with maximum degree 4.
References
SHOWING 1-10 OF 39 REFERENCES
On a conjecture by Plummer and Toft
- Mathematics
- 1999
The cyclic chromatic number χc(G) of a 2-connected plane graph G is the minimum number of colors in an assigment of colors to the vertices of G such that, for every face-bounding cycle f of G, the…
On vertex types and cyclic colourings of 3-connected plane graphs
- MathematicsDiscret. Math.
- 2000
A New Bound on the Cyclic Chromatic Number
- MathematicsJ. Comb. Theory, Ser. B
- 2001
In 1969, Ore and Plummer defined an angular coloring as a natural extension of the Four Color Problem: a face coloring of a plane graph where faces meeting even at a vertex must have distinct colors.…
A new proof of the 6 color theorem
- MathematicsJ. Graph Theory
- 1995
A shorter new proof is given here using only half as many of reducible configurations of the 6 color problem for graphs that can be stated in at least three different forms.
3-Facial Coloring of Plane Graphs
- MathematicsSIAM J. Discret. Math.
- 2008
It is proved that every plane graph is $3$-facially $11$-colorable and derived that every $2$-connected plane graph with maximum face-size at most $7$ is cyclically cyclically colorable.