The chordless cycle polynomial of a graph may be defined as
 |
where 
is the number of chordless cycles (of length at
least four) and 
is the length of a longest chordless
cycle.
Precomputed chordless cycles of many graphs are implemented in the Wolfram Language as GraphData[g, "ChordlessCyclePolynomial"][x].
If 
is a bipartite graph, then 
contains only even powers
of 
because the length of every graph cycle in 
is an even number. By König's
line coloring theorem, the same conclusion holds when 
has a bipartite graph as
its root graph, even though 
need not itself be a bipartite
graph. In this case every chordless cycle
of length at least 4 comes from a graph cycle in the
root graph, while triangles
in 
are not counted by 
. Consequently, the odd part
of 
is 0 for both bipartite graphs and line
graphs of bipartite graphs.
