pgr_edgeColoring  Experimental¶
pgr_edgeColoring
— Returns the edge coloring of an undirected and loopfree (i.e no selfloops and no parallel edges) graph.
Warning
Possible server crash
These functions might create a server crash
Warning
Experimental functions
They are not officially of the current release.
They likely will not be officially be part of the next release:
The functions might not make use of ANYINTEGER and ANYNUMERICAL
Name might change.
Signature might change.
Functionality might change.
pgTap tests might be missing.
Might need c/c++ coding.
May lack documentation.
Documentation if any might need to be rewritten.
Documentation examples might need to be automatically generated.
Might need a lot of feedback from the comunity.
Might depend on a proposed function of pgRouting
Might depend on a deprecated function of pgRouting
Availability
Version 3.3.0
New experimental function
Description¶
Edge Coloring is an algorithm used for coloring of the edges for the vertices in the graph. It is an assignment of colors to the edges of the graph so that no two adjacent edges have the same color.
The main Characteristics are:
The implementation is applicable only for undirected and loopfree (i.e no selfloops and no parallel edges) graphs.
Provides the color to be assigned to all the edges present in the graph.
At most Δ + 1 colors are used, where Δ is the degree of the graph. This is optimal for some graphs, and by Vizing’s theorem it uses at most one color more than the optimal for all others.
It can tell us whether a graph is Bipartite. If in a graph, the chromatic number χ′(G) i.e. minimum number of colors needed for proper edge coloring of graph is equal to degree Δ of the graph, (i.e. χ′(G) = Δ) then graph is said to be Bipartite. But, the viceversa is not always true.
The algorithm tries to assign the least possible color to every edge.
Efficient graph coloring is an NPHard problem, and therefore, this algorithm does not always produce optimal coloring.
The returned rows are ordered in ascending order of the edge value.
This algorithm is the fastest known almostoptimal algorithm for edge coloring.
Edge Coloring Running Time: \(O(EV)\)
where \(E\) is the number of edges in the graph,
\(V\) is the number of vertices in the graph.
Signatures¶
pgr_edgeColoring(Edges SQL)
RETURNS SET OF (edge_id, color_id)
OR EMPTY SET
 Example
Graph coloring of pgRouting Sample Data
SELECT * FROM pgr_edgeColoring(
'SELECT id, source, target, cost, reverse_cost FROM edge_table
ORDER BY id'
);
edge_id  color_id
+
1  3
2  2
3  3
4  4
5  4
6  1
7  2
8  1
9  2
10  5
11  5
12  3
13  2
14  1
15  3
16  1
17  1
18  1
(18 rows)
Parameters¶
Parameter 
Type 
Description 

Edges SQL 

Inner query as described below. 
Inner query¶
 Edges SQL
an SQL query of an undirected graph, which should return a set of rows with the following columns:
Column 
Type 
Default 
Description 

id 

Identifier of the edge. 

source 

Identifier of the first end point vertex of the edge. 

target 

Identifier of the second end point vertex of the edge. 

cost 



reverse_cost 

1 

Where:
 ANYINTEGER
SMALLINT, INTEGER, BIGINT
 ANYNUMERICAL
SMALLINT, INTEGER, BIGINT, REAL, FLOAT
Result Columns¶
Returns SET OF (edge_id, color_id)
Column 
Type 
Description 

edge_id 

Identifier of the edge. 
color_id 

Identifier of the color of the edge.

See Also¶
The queries use the Sample Data network.
Indices and tables