We consider simple connected graphs for which there is a path of length at least k between every pair of distinct vertices. We wish to show that in these graphs the cycle space over $\mathbb{Z}_2$ is generated by the cycles of length at least $mk$, where $m = 1$ for $3 \le k \le 6$, $m = 6/7$ for $k = 7$, $m \ge 1/2$ for $k \ge 8$ and $m \le 3/4 + 0(1)$ for large k.

k-path connectivity and mk-generation, an upper bound

ABREU, Marien;
2006

Abstract

We consider simple connected graphs for which there is a path of length at least k between every pair of distinct vertices. We wish to show that in these graphs the cycle space over $\mathbb{Z}_2$ is generated by the cycles of length at least $mk$, where $m = 1$ for $3 \le k \le 6$, $m = 6/7$ for $k = 7$, $m \ge 1/2$ for $k \ge 8$ and $m \le 3/4 + 0(1)$ for large k.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11563/7815
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