207,068 research outputs found
Contractions, Removals and How to Certify 3-Connectivity in Linear Time
It is well-known as an existence result that every 3-connected graph G=(V,E)
on more than 4 vertices admits a sequence of contractions and a sequence of
removal operations to K_4 such that every intermediate graph is 3-connected. We
show that both sequences can be computed in optimal time, improving the
previously best known running times of O(|V|^2) to O(|V|+|E|). This settles
also the open question of finding a linear time 3-connectivity test that is
certifying and extends to a certifying 3-edge-connectivity test in the same
time. The certificates used are easy to verify in time O(|E|).Comment: preliminary versio
A generating function for the cubic interactions of higher spin fields
We present an off-shell generating function for all cubic interactions of
Higher Spin gauge fields constructed in arXiv:1003.2877. It is a generalization
of the on-shell generating function proposed in arXiv:1006.5242, is written in
a very compact way, and turns out to have a remarkable structure.Comment: 14 pages, Latex,v.2 misprints corrected, v.3 ref. added, v. 4
published in Phys. Lett.
Path-factors involving paths of order seven and nine
In this paper, we show the following two theorems (here is the
number of components of with ): (i)~If a graph
satisfies for all , then has a
-factor. (ii)~If a graph satisfies
for all , then has a
-factor.Comment: 29 pages, 4 figure
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