8 papers
Balanced-chromatic number and Hadwiger-like conjectures
Andrea Jiménez, Jessica McDonald, Reza Naserasr +2
Motivated by different characterizations of planar graphs and the 4-Color Theorem, several structural results concerning graphs of high chromatic number have been obtained. Toward…
Winding number and circular coloring
Reza Naserasr, Cyril Pujol, Lujia Wang
In 1996, Youngs proved a surprising theorem that quadrangulations of the projective plane could never have chromatic number exactly 3. This sparked a lot of interest, and the resul…
Extension of the Gyárfás-Sumner conjecture to signed graphs
Guillaume Aubian, Allen Ibiapina, Luis Kuffner +4
The balanced chromatic number of a signed graph G is the minimum number of balanced sets that cover all vertices of G. Studying structural conditions which imply bounds on the bala…
Brooks' theorem for signed graphs with
Reza Naserasr, Huan Zhou
Circular -coloring of a signed graph is a mapping of its vertices to a circle of circumference such that: I. each pair of vertices with a negative connection is at…
Colouring signed analogues of Kneser, Schrijver, and Borsuk graphs
Luis Kuffner, Reza Naserasr, Lujia Wang +3
The Kneser signed graph $\KS(n,k)$, , is the graph whose vertices are signed -subsets of (i.e. -subsets of such that $S\…
Fractional balanced chromatic number and arboricity of planar (signed) graphs
Reza Naserasr, Lan Anh Pham, Cyril Pujol +1
A fractional coloring of a signed graph is an assignment of nonnegative weights to the balanced sets (sets which do not induce a negative cycle) such that each vertex has…