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COMBINATORICS
2004
13 years 9 months ago
2004
The basic functional equations for connected and 2-connnected graphs can be traced back to the statistical physicists Mayer and Husimi. They play an essential role in establishing...
COMBINATORICS
2004
13 years 9 months ago
2004
For every real p > 0 and simple graph G, set f (p, G) = uV (G) dp (u) , and let (r, p, n) be the maximum of f (p, G) taken over all Kr+1-free graphs G of order n. We prove tha...
COMBINATORICS
2004
13 years 9 months ago
2004
We extend Schaeffer's bijection between rooted quadrangulations and welllabeled trees to the general case of Eulerian planar maps with prescribed face valences to obtain a bi...
COMBINATORICS
2004
13 years 9 months ago
2004
We consider Class-Uniformly Resolvable frames (CURFs), which are group divisible designs with partial resolution classes subject to the class-uniform condition. We derive the nece...
COMBINATORICS
2004
13 years 9 months ago
2004
When can a d-dimensional rectangular box R be tiled by translates of two given d-dimensional rectangular bricks B1 and B2? We prove that R can be tiled by translates of B1 and B2 ...