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JCT
2006
14 years 9 months ago
2006
We prove that the anisotropic generating function of self-avoiding polygons is not a D-finite function--proving a conjecture of Guttmann [Discrete Math. 217 (2000) 167
JCT
2006
14 years 9 months ago
2006
We find the graphs of valency at most 7 with the property that any two nonadjacent vertices have either 0 or 2 common neighbours. In particular, we find all semibiplanes of block ...
JCT
2006
14 years 9 months ago
2006
: We prove that in PG(3, q), q > 19, a partial flock of a quadratic cone with q - planes, can be extended to a unique flock if < 1 4 q.
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JCT
2006
14 years 9 months ago
2006
We give a combinatorial proof of the first Rogers-Ramanujan identity by using two symmetries of a new generalization of Dyson's rank. These symmetries are established by direc...
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JCT
2006
14 years 9 months ago
2006
: We prove that every triangle-free planar graph on n vertices with maximum degree three has an independent set with size at least 3 8 n. This was suggested and later conjectured b...