Bounds for the Zero-Forcing Number of Graphs with Large Girth
نویسندگان
چکیده
We investigate the zero-forcing number for triangle-free graphs. We improve upon the trivial bound, δ ≤ Z(G) where δ is the minimum degree, in the triangle-free case. In particular, we show that 2δ− 2 ≤ Z(G) for graphs with girth of at least 5, and this can be further improved when G has a small cut set. Lastly, we make a conjecture that the lower bound for Z(G) increases as a function of the girth, g, and δ.
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ورودعنوان ژورنال:
- CoRR
دوره abs/1406.0482 شماره
صفحات -
تاریخ انتشار 2014