Patterns radiating out from a center point can be tricky and have, in the past, resulted in some rather creative outbursts from me on more than one occasion (fortunately no one was in ear shot to hear me on those occassions). But there are a few things you can do to avoid chip out at the centre.
First off, make sure your knife is, as Marty says, scary sharp. For tight patterns like at the centre of the luggage tag I find using the modified knife works best.
Now you don’t need to have every chip radiating out from the very center of the pattern. Trying to have each trip starting from the very center is guaranteed to result in chip out (and probably some creative loud outbursts). Instead you want to offset some of the chips away from the center point. I find offsetting every other chip has worked for me but I don’t know if there is a hard and fast rule on a sequence for staggering offset chips. I try to randomly stagger the offsets to avoid creating a pattern and taking away from the center effect.
Of course you also want to remember to smoothly draw the tip of the blade out (go shallow) as you cut towards the center to avoid undercutting.
The final thing to do is plan out your order of cuts from your very first cut of your first chip so that as you work around the radiating pattern the last cut of your last chip will be with the grain.
With a bit of practice I have found that I don’t need to worry about creative outbursts or Super Glue at all. For a great example of this technique, check out Marty’s video for carving a swirl rosette.
Hope this helps.