# Partition of a cubic 3-connected graphs into paths of length 2.

**Problem**Does every -connected cubic graph on vertices admit a partition into paths of length ?

More generally, the following question is posed.

**Problem**Does every -connected cubic graph on at least vertices contain pairwise vertex-disjoint paths of length ?

In [K1], Kelmans gave a construction that provided infinitely many 2-connected graphs for which the above statement is false.

## Bibliography

[K1] Alexander K. Kelmans, Packing 3-vertex paths in 2-connected graphs

*[K2] Alexander K. Kelmans, On --Packing in 3--connected Graphs, RUTCOR Research Report 23--2005, Rutgers University. See also Packing 3-vertex Paths In Cubic 3-connected Graphs

* indicates original appearance(s) of problem.