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7365 Petersen's 2-factor theorem ncohen rlm "As the docstring says :
Petersen's 2-factor decomposition theorem asserts that any
`2r`-regular graph `G` can be decomposed into 2-factors.
Equivalently, it means that the edges of any `2r`-regular
graphs can be partitionned in `r` sets `C_1,\dots,C_r` such
that for all `i`, the set `C_i` is a disjoint union of cycles
( a 2-regular graph ).
As any graph of maximal degree `\Delta` can be completed into
a regular graph of degree `2\lceil\frac\Delta 2\rceil`, this
result also means that the edges of any graph of degree `\Delta`
can be partitionned in `r=2\lceil\frac\Delta 2\rceil` sets
`C_1,\dots,C_r` such that for all `i`, the set `C_i` is a
graph of maximal degree 2 ( a disjoint union of paths
and cycles ).
Nathann" enhancement closed major sage-4.3 graph theory fixed sage-4.3.rc1 Nathann Cohen Robert Miller N/A