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Possible Bug within GraphData?

António Pereira
Posted 10 years ago

I'm trying to get graphs with no perfect matching of order 26 using GraphData. It seems that GraphData["NoPerfectMatching", 26] returns several graphs that have a Perfect Matching ( NoncayleyTransite graphs). I'm using Mathematica 10.3. I've filled a bug to Wolfram support, but I'd appreciate if someone can confirm the following output.

Thanks in advance A. Pereira

In[1]:= l = GraphData["NoPerfectMatching", 26];

In[2]:= GraphData[#, "PerfectMatching"] & /@ l

Out[2]= {False, False, False, False, True, True, True, True, True, \
True, True, True, True, True, True, True, True, True, True, True, \
True, True, True, True, True, True, True, True, True, True, True, \
True, True, True, True, True, True, True, True, True, True, True, \
True, True, True, True, True, True, True, True, True, True, True, \
True, True, True, True, True, True, True, True, True, True, True, \
True, True, True, True, True, True, True, True, True, False, False}
POSTED BY: António Pereira
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Seems like Wolfram has updated the GraphData database and today it list correctly only graphs with a perfect matching:

In[1]:= GraphData["NoPerfectMatching", 26]

Out[1]= {{"CayleyTree", {5, 2}}, "DeltoidalIcositetrahedralGraph", {"DutchWindmill", {5, 
   6}}, {"Empty", 26}, "Octane", {"Windmill", {5, 6}}}

So my problem is solved for now. Lesson learned: Never trust 100% on data that is not yours. And even if it is your data, check and recheck, for consistency!
POSTED BY: António Pereira 
GraphData["NoPerfectMatching", 26];

In this way, there is a result(profit).
POSTED BY: Simon Cadrin

Thank you for the reply. Now I know this is not a problem of my install.

POSTED BY: António Pereira

Yes. I get the same output. The developers were able to reproduce the issue and are looking into how to resolve it. Thank you for taking the time to let us know about this issue.

POSTED BY: Sean Clarke
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