Matches in SemOpenAlex for { <https://semopenalex.org/work/W2756730563> ?p ?o ?g. }
Showing items 1 to 80 of
80
with 100 items per page.
- W2756730563 abstract "The representation complexity of a bipartite graph $G=(P,Q)$ is the minimum size $sum_{i=1}^s (|A_i|+|B_i|)$ over all possible ways to write $G$ as a (not necessarily disjoint) union of complete bipartite subgraphs $G=cup_{i=1}^s A_itimes B_i$ where $A_isubset P, B_isubset Q$ for $i=1,dots, s$. In this paper we prove that if $G$ is emph{semi-algebraic}, i.e. when $P$ is a set of $m$ points in $mathbb{R}^{d_1}$, $Q$ is a set of $n$ points in $mathbb{R}^{d_2}$ and the edges are defined by some semi-algebraic relations, the representation complexity of $G$ is $O( m^{frac{d_1d_2-d_2}{d_1d_2-1}+varepsilon} n^{frac{d_1d_2-d_1}{d_1d_2-1}+varepsilon}+m^{1+varepsilon}+n^{1+varepsilon})$ for arbitrarily small positive $varepsilon$. This generalizes results by Apfelbaum-Sharir and Solomon-Sharir. As a consequence, when $G$ is $K_{u,u}$-free for some positive integer $u$, its number of edges is $O(u m^{frac{d_1d_2-d_2}{d_1d_2-1}+varepsilon} n^{frac{d_1d_2-d_1}{d_1d_2-1}+varepsilon}+ u m^{1+varepsilon}+u n^{1+varepsilon})$. This bound is stronger than that of Fox, Pach, Sheffer, Suk and Zahl when the first term dominates and $u$ grows with $m,n$. Another consequence is that we can find a large complete bipartite subgraph in a semi-algebraic graph when the number of edges is large. Similar results hold for semi-algebraic hypergraphs." @default.
- W2756730563 created "2017-10-06" @default.
- W2756730563 creator A5059018536 @default.
- W2756730563 date "2017-09-24" @default.
- W2756730563 modified "2023-09-27" @default.
- W2756730563 title "Representation Complexity of Semi-algebraic Graphs" @default.
- W2756730563 cites W1481710404 @default.
- W2756730563 cites W1972978715 @default.
- W2756730563 cites W1991581432 @default.
- W2756730563 cites W2034834286 @default.
- W2756730563 cites W2101788557 @default.
- W2756730563 cites W2109298068 @default.
- W2756730563 cites W2110354774 @default.
- W2756730563 cites W2130760369 @default.
- W2756730563 cites W2166961358 @default.
- W2756730563 cites W2234407461 @default.
- W2756730563 cites W2244396186 @default.
- W2756730563 cites W2300360267 @default.
- W2756730563 cites W2336392368 @default.
- W2756730563 cites W2480148066 @default.
- W2756730563 cites W2613470006 @default.
- W2756730563 cites W2963208722 @default.
- W2756730563 hasPublicationYear "2017" @default.
- W2756730563 type Work @default.
- W2756730563 sameAs 2756730563 @default.
- W2756730563 citedByCount "1" @default.
- W2756730563 countsByYear W27567305632019 @default.
- W2756730563 crossrefType "posted-content" @default.
- W2756730563 hasAuthorship W2756730563A5059018536 @default.
- W2756730563 hasConcept C114614502 @default.
- W2756730563 hasConcept C118615104 @default.
- W2756730563 hasConcept C132525143 @default.
- W2756730563 hasConcept C134306372 @default.
- W2756730563 hasConcept C197657726 @default.
- W2756730563 hasConcept C199360897 @default.
- W2756730563 hasConcept C33923547 @default.
- W2756730563 hasConcept C41008148 @default.
- W2756730563 hasConcept C45340560 @default.
- W2756730563 hasConcept C77553402 @default.
- W2756730563 hasConcept C9376300 @default.
- W2756730563 hasConcept C97137487 @default.
- W2756730563 hasConceptScore W2756730563C114614502 @default.
- W2756730563 hasConceptScore W2756730563C118615104 @default.
- W2756730563 hasConceptScore W2756730563C132525143 @default.
- W2756730563 hasConceptScore W2756730563C134306372 @default.
- W2756730563 hasConceptScore W2756730563C197657726 @default.
- W2756730563 hasConceptScore W2756730563C199360897 @default.
- W2756730563 hasConceptScore W2756730563C33923547 @default.
- W2756730563 hasConceptScore W2756730563C41008148 @default.
- W2756730563 hasConceptScore W2756730563C45340560 @default.
- W2756730563 hasConceptScore W2756730563C77553402 @default.
- W2756730563 hasConceptScore W2756730563C9376300 @default.
- W2756730563 hasConceptScore W2756730563C97137487 @default.
- W2756730563 hasLocation W27567305631 @default.
- W2756730563 hasOpenAccess W2756730563 @default.
- W2756730563 hasPrimaryLocation W27567305631 @default.
- W2756730563 hasRelatedWork W1802317609 @default.
- W2756730563 hasRelatedWork W2130270608 @default.
- W2756730563 hasRelatedWork W2150193181 @default.
- W2756730563 hasRelatedWork W2234407461 @default.
- W2756730563 hasRelatedWork W2311250512 @default.
- W2756730563 hasRelatedWork W2520302603 @default.
- W2756730563 hasRelatedWork W2768930897 @default.
- W2756730563 hasRelatedWork W2803584453 @default.
- W2756730563 hasRelatedWork W2951723736 @default.
- W2756730563 hasRelatedWork W2952277897 @default.
- W2756730563 hasRelatedWork W2963969197 @default.
- W2756730563 hasRelatedWork W2963997401 @default.
- W2756730563 hasRelatedWork W2969799327 @default.
- W2756730563 hasRelatedWork W2980245002 @default.
- W2756730563 hasRelatedWork W2995452317 @default.
- W2756730563 hasRelatedWork W3083711241 @default.
- W2756730563 hasRelatedWork W3090797620 @default.
- W2756730563 hasRelatedWork W3102192770 @default.
- W2756730563 hasRelatedWork W3127987152 @default.
- W2756730563 hasRelatedWork W3164872525 @default.
- W2756730563 isParatext "false" @default.
- W2756730563 isRetracted "false" @default.
- W2756730563 magId "2756730563" @default.
- W2756730563 workType "article" @default.