0 KB295 KB30 KB200820252011Streinu, IleanaTheran, Louisštevilka:1letnik:4str. 141-151COBISSID:16265561ISSN:1855-3966URN:URN:NBN:SI:doc-KLFC1CH3enDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneacombinatorial rigiditygraph theorykombinatorična rigidnostmatroidimatroidsredki grafiredki hipergrafisparse graphssparse hypergraphsteorija grafovNatural realizations of sparsity matroids|A hypergraph ?$G$? with ?$n$? vertices and ?$m$? hyperedges with ?$d$? endpoints each is ?$(k,\ell )$?-sparse if for all sub-hypergraphs ?$G^\prime$? on ?$n^\prime$? vertices and ?$m^\prime$? edges, ?$m^\prime \leq kn^\prime - \ell$?. For integers ?$k$? and ?$\ell$? satisfying ?$0 \leq \ell \leq dk - 1$?, this is known to be a linearly representable matroidal family. Motivated by problems in rigidity theory, we give a new linear representation theorem for the ?$(k,\ell)$?-sparse hypergraphs that is natural; i.e., the representing matrix captures the vertex-edge incidence structure of the underlying hypergraph ?$G$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije