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DM
2010
13 years 10 months ago
2010
For a non-negative integer T, we prove that the independence number of a graph G = (V, E) in which every vertex belongs to at most T triangles is at least uV f(d(u), T) where d(u)...
DM
2010
13 years 10 months ago
2010
Let Mad(G) denote the maximum average degree (over all subgraphs) of G and let i(G) denote the injective chromatic number of G. We prove that if Mad(G) 5 2 , then i(G) + 1; sim...
DM
2010
13 years 10 months ago
2010
A generalization of the Davenport constant is investigated. For a finite abelian group G and a positive integer k, let Dk(G) denote the smallest such that each sequence over G of l...
DM
2010
13 years 10 months ago
2010
When the standard representation of a crystallographic Coxeter group G (with string diagram) is reduced modulo the integer d 2, one obtains a finite group Gd often the automorphi...
DM
2010
13 years 10 months ago
2010
Let H 2V be a hypergraph on vertex set V . For a positive integer r, we call H r-exact, if any minimal transversal of H intersects any hyperedge of H in at most r vertices. This ...