• Corpus ID: 235390730

Symmetric set coloring of signed graphs

  title={Symmetric set coloring of signed graphs},
  author={Chiara Cappello and Eckhard Steffen},
There are many approaches to signed graphs coloring. One of the main difference regards the number of self-inverse elements used. We develop a new coloring by using symmetric sets with different numbers of self-inverse elements. This approach provides a framework to describe all other ways of coloring signed graphs which are defined by assigning colors to the vertices of the graphs. We investigate the specific role of self-inverse colors in signed graph coloring and prove a Brooks’ type theorem… 

Figures from this paper

Bounds for the chromatic index of signed multigraphs

The paper studies edge-coloring of signed multigraphs and extends classical Theo-rems of Shannon [6] and K¨onig [4] to signed multigraphs. We prove that the chromatic index of a signed multigraph (



Signed graph coloring

Circular coloring of signed graphs

The well studied notions of $(k,d)-colorings and of the circular chromatic number $\chi_c$ to signed graphs are generalized, which implies a new notion of colorings of signed graphs, and the corresponding chromaticNumber $\chi$.

How colorful the signed graph?

Coloring permutation-gain graphs

This note state how correspondence colorings generalize Zaslavsky's notion of gain-graph colorings and then formulate a new coloring theory of permutation-gain graphs that sits between gain- graph coloring and correspondence coloring.

On DP-coloring of graphs and multigraphs

While solving a question on the list coloring of planar graphs, Dvořák and Postle introduced the new notion of DP-coloring (they called it correspondence coloring). A DP-coloring of a graph G reduces

The Chromatic Number of a Signed Graph

The definition of a chromatic number for signed graphs is proposed which provides a natural extension of thechromatic number of an unsigned graph and is establish the basic properties of this invariant.

Circular Chromatic Number of Signed Graphs

The supremum of the signed circular chromatic number of k-chromatic graphs of large girth, of simple bipartite planar graphs, d-degenerate graphs, simple outerplanar graphs and series-parallel graphs is determined.

On colouring the nodes of a network

  • R. L. Brooks
  • Mathematics, Computer Science
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1941
Let N be a network (or linear graph) such that at each node not more than n lines meet (where n > 2), and no line has both ends at the same node. Suppose also that no connected component of N is an