𝔖 Bobbio Scriptorium
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A conjecture concerning the ranking of the sciences

✍ Scribed by Paul Humphreys


Book ID
111703749
Publisher
Springer Netherlands
Year
1990
Tongue
English
Weight
365 KB
Volume
9
Category
Article
ISSN
0167-7411

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## Abstract We give a plausible‐sounding conjecture involving the number of __n__‐equivalence classes of structures of size __m__ which would imply that the complement of a spectrum is also a spectrum. Mathematics Subject Classification: 03B10, 03D15, 68Q15.

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It has been conjectured by C. van Nuffelen that the chromatic number of any graph with at least one edge does not exceed the rank of its adjacency matrix. We give a counterexample, with chromatic number 32 and with an adjacency matrix of rank 29.