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number theory
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Problem ledger
2 problems
Graph view
declared open
· formalized · $500
erdos:593
Which finite triple systems occur in every triple system of uncountable chromatic number? The claimed characterization: exactly those that, after removing isolated vertices, are linear, have every hyperedge-node of their Levi graph meeting a bridge, and have every Berge cycle even.
set theory
graph theory
hypergraphs
N/A
4 sources
declared open
erdos:1177
For a finite forbidden triple system
G
G
, what exact uncountable chromatic cardinalities occur among
G
G
-free triple systems, and how do those spectra interact? The revised manuscript answers the three exact-cardinal questions and claims a complete spectrum dichotomy.
set theory
chromatic number
hypergraphs
N/A
3 sources
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