#9619: b-coloring of a graph
----------------------------+-----------------------------------------------
Reporter: lsampaio | Owner: jason, ncohen, rlm
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.5.2
Component: graph theory | Keywords:
Author: lsampaio | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
----------------------------+-----------------------------------------------
This patch adds the function b_coloring, which computes a b-coloring with
the maximum number of colors. Here are some explanations from the
function's help :
Given a proper coloring of a graph G and a color class C such that
none of its vertices have neighbors in all the other color classes, one
can eliminate color class C by assigning distinct colors to each of its
elements.
One can repeat this procedure until a coloring is obtained where every
color class contains one vertex with neighbors in all the other color
classes. We call such a vertex a b-vertex. So, one can define a b-coloring
as a proper coloring where each color class has a b-vertex, a vertex with
neighbors in all the other colors.
The worst-case behaviour of this procedure for eliminating color
classes is the b-chromatic number of G (denoted \chi_b(G)): the maximum k
such that G admits a b-coloring with k colors.
Leonardo
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9619>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
