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JCT
2007
140views more  JCT 2007»
13 years 3 months ago
Homomorphisms and edge-colourings of planar graphs
We conjecture that every planar graph of odd-girth 2k + 1 admits a homomorphism to Cayley graph C(Z2k+1 2 , S2k+1), with S2k+1 being the set of (2k + 1)vectors with exactly two co...
Reza Naserasr
JCT
2007
64views more  JCT 2007»
13 years 3 months ago
The roots of the independence polynomial of a clawfree graph
Maria Chudnovsky, Paul D. Seymour
JCT
2007
122views more  JCT 2007»
13 years 3 months ago
h-Vectors of Gorenstein polytopes
We show that the Ehrhart h-vector of an integer Gorenstein polytope with a unimodular triangulation satisfies McMullen’s g-theorem; in particular it is unimodal. This result gen...
Winfried Bruns, Tim Römer
JCT
2007
103views more  JCT 2007»
13 years 3 months ago
Geometric drawings of Kn with few crossings
We give a new upper bound for the rectilinear crossing number cr(n) of the complete geometric graph Kn. We prove that cr(n) ≤ 0.380559 ¡n 4 ¢ + Θ(n3 ) by means of a new const...
Bernardo M. Ábrego, Silvia Fernández...
JCT
2007
112views more  JCT 2007»
13 years 3 months ago
On generalized Kneser hypergraph colorings
In Ziegler (2002), the second author presented a lower bound for the chromatic numbers of hypergraphs KGr sssS, “generalized r-uniform Kneser hypergraphs with intersection multi...
Carsten E. M. C. Lange, Günter M. Ziegler
JCT
2007
111views more  JCT 2007»
13 years 3 months ago
Lattice point counts for the Shi arrangement and other affinographic hyperplane arrangements
Hyperplanes of the form xj = xi + c are called affinographic. For an affinographic hyperplane arrangement in Rn, such as the Shi arrangement, we study the function f(m) that counts...
David Forge, Thomas Zaslavsky
JCT
2007
83views more  JCT 2007»
13 years 3 months ago
A finiteness theorem for Markov bases of hierarchical models
We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimen...
Serkan Hosten, Seth Sullivant
JCT
2007
83views more  JCT 2007»
13 years 3 months ago
On 6-sparse Steiner triple systems
We give the first known examples of 6-sparse Steiner triple systems by constructing 29 such systems in the residue class 7 modulo 12, with orders ranging from 139 to 4447. We the...
A. D. Forbes, Mike J. Grannell, Terry S. Griggs
JCT
2007
92views more  JCT 2007»
13 years 3 months ago
Minimal non-orientable matroids in a projective plane
: We construct a new family of minimal non-orientable matroids of rank three. Some of these matroids embed in Desarguesian projective planes. This answers a question of Ziegler: fo...
Rigoberto Flórez, David Forge