On the signed chromatic number of some classes of graphs

@article{Bensmail2022OnTS,
  title={On the signed chromatic number of some classes of graphs},
  author={Julien Bensmail and Sandip Das and Soumen Nandi and Th{\'e}o Pierron and Sagnik Sen and {\'E}ric Sopena},
  journal={Discret. Math.},
  year={2022},
  volume={345},
  pages={112664}
}
View PDF on arXiv
3 Citations
Background Citations
1

Figures from this paper

3 Citations

Citation Type

Citation Type

On the chromatic numbers of signed triangular and hexagonal grids
The chromatic number of signed graphs with bounded maximum average degree
TLDR
The chromatic number χs(G) of a signed graph G is the order of a smallest signed graph H such that there is a homomorphism from G to H .
The chromatic number of signed graphs with bounded maximum average degree

References

SHOWING 1-10 OF 34 REFERENCES
Homomorphisms of signed graphs: An update
Classification of edge-critical underlying absolute planar cliques for signed graphs
A simple signed graph (G,Σ) is a simple graph G having two different types of edges, positive edges and negative edges, where Σ denotes the set of negative edges of G. A closed walk of a signed graph…
The complexity of signed graph and edge-coloured graph homomorphisms
Homomorphisms of Edge-Colored Graphs and Coxeter Groups
AbstractLet $$G_1 = (V_1 ,E_1 ){\text{ and }}G_2 = (V_2 ,E_2 )$$ be two edge-colored graphs (without multiple edges or loops). A homomorphism is a mappingϕ : $$V_1 \mapsto V_2 $$ for which, for…
Homomorphisms of Signed Graphs
TLDR
This paper is the first general study of signed graph homomorphisms, and reformulating Hadwiger's conjecture in the language of homomorphism of signed graphs whose underlying graph is bipartite shows that while some stronger form of the conjecture holds for small chromatic number, such strengthening of the conjectures would not hold for large chromatic numbers.
Relative Clique Number of Planar Signed Graphs
TLDR
The exact values of signed relative clique number of the families of outerplanar graphs and triangle-free planar graphs are determined.
Walk-Powers and Homomorphism Bounds of Planar Signed Graphs
TLDR
This work shows that if the conjecture that every planar graph of odd-girth at least 2k admits a homomorphism to the projective cube of dimension 2k is true, then PC(2k) is an optimal such graph both with respect to the number of vertices and theNumber of edges.
Acyclic and oriented chromatic numbers of graphs
TLDR
This paper discusses the relations between the oriented chromatic number and the acyclic chromatic numbers and some other parameters of a graph and gives a lower bound for χo(G) in terms of χa(G).
Pushable chromatic number of graphs with degree constraints
On Chromatic Number of Colored Mixed Graphs
TLDR
The acyclic chromatic number of a graph is bounded by k(2) k( 2+) inverted left perpedicular log((2m+n) log(2m-n) k inverted right perpendicular if its (m, n)-colored mixed Chromatic number is at most k.
...
...