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JCT
2010
14 years 8 months ago
2010
In 1978, Chv´atal and Thomassen proved that every 2-edge-connected graph with diameter 2 has an orientation with diameter at most 6. They also gave general bounds on the smallest...
JCT
2010
14 years 8 months ago
2010
A lattice path matroid is a transversal matroid for which some antichain of intervals in some linear order on the ground set is a presentation. We characterize the minor-closed cla...
JCT
2010
14 years 8 months ago
2010
We prove that for every k and every ε > 0, there exists g such that every graph with tree-width at most k and odd-girth at least g has circular chromatic number at most 2 + ε...
JCT
2010
14 years 8 months ago
2010
We prove a vector space analog of a version of the Kruskal-Katona theorem due to Lov´asz. We apply this result to extend Frankl’s theorem on r-wise intersecting families to vec...
JCT
2010
14 years 8 months ago
2010
Combinatorial proofs are given for certain entries in Ramanujan’s lost notebook. Bijections of Sylvester, Franklin, Wright, and Yee are employed. A new bijection, involving the n...