1 research outputs found
Nowhere-zero flows on signed regular graphs
We study the flow spectrum and the integer flow spectrum
of signed -regular graphs. We show that if , then or .
Furthermore, if and only if has a
-factor. If has a 1-factor, then , and for
every , there is a signed -regular graph with and does not have a 1-factor.
If is a cubic graph which has a 1-factor, then . Furthermore, the following
four statements are equivalent: (1) has a 1-factor. (2) . (3) . (4) .
There are cubic graphs whose integer flow spectrum does not contain 5 or 6, and
we construct an infinite family of bridgeless cubic graphs with integer flow
spectrum .
We show that there are signed graphs where the difference between the integer
flow number and the flow number is greater than or equal to 1, disproving a
conjecture of Raspaud and Zhu.
The paper concludes with a proof of Bouchet's 6-flow conjecture for
Kotzig-graphs.Comment: 24 pages, 4 figures; final version; to appear in European J.
Combinatoric