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Dividing up the unrestricted partitions ★★
Begin with the generating function for unrestricted partitions:
(1+x+x^2+...)(1+x^2+x^4+...)(1+x^3+x^6+...)...
Now change some of the plus signs to minus signs. The resulting series will have coefficients congruent, mod 2, to the coefficients of the generating series for unrestricted partitions. I conjecture that the signs may be chosen such that all the coefficients of the series are either 1, -1, or zero.
Keywords: congruence properties; partition
Finding k-edge-outerplanar graph embeddings ★★
Author(s): Bentz
Conjecture It has been shown that a 
-outerplanar embedding for which is minimal can be found in polynomial time. Does a similar result hold for -edge-outerplanar graphs?
-outerplanar embedding for which is minimal can be found in polynomial time. Does a similar result hold for -edge-outerplanar graphs? Keywords: planar graph; polynomial algorithm
Approximation ratio for k-outerplanar graphs ★★
Author(s): Bentz
Conjecture Is the approximation ratio for the Maximum Edge Disjoint Paths (MaxEDP) or the Maximum Integer Multiflow problem (MaxIMF) bounded by a constant in -outerplanar graphs or tree-width graphs?
-outerplanar graphs or tree-width graphs? Keywords: approximation algorithms; planar graph; polynomial algorithm
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